arXiv subjects

Vassilis Kekatos

Publications and source records attributed to Vassilis Kekatos.

At least 55 records · Page 3Linked to original sources

arXiv2020

Joint Grid Topology Reconfiguration and Design of Watt-VAR Curves for DERs

Operators can now remotely control switches and update the control settings for voltage regulators and distributed energy resources (DERs), thus unleashing the network reconfiguration opportunities to improve efficiency. Aligned to this direction, this work puts forth a comprehensive toolbox of optimization models leveraging the control capabilities of smart grid assets. We put forth detailed yet practical models to capture the operation of locally and remotely controlled regulators, and customize the watt-var DER control curves complying with the IEEE 1547.8 mandates. Maintaining radiality is a key requirement germane to various feeder optimization tasks. This requirement is accomplished here through an intuitive and provably correct formulation. The developed toolbox is put into action to reconfigure a grid for minimizing losses using real-world data on a benchmark feeder. The results corroborate that optimal topologies vary across the day and coordinating DERs and regulators is critical during periods of steep net load changes.

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arXiv2020

Natural Gas Flow Solvers using Convex Relaxation

The vast infrastructure development, gas flow dynamics, and complex interdependence of gas with electric power networks call for advanced computational tools. Solving the equations relating gas injections to pressures and pipeline flows lies at the heart of natural gas network (NGN) operation, yet existing solvers require careful initialization and uniqueness has been an open question. In this context, this work considers the nonlinear steady-state version of the gas flow (GF) problem. It first establishes that the solution to the GF problem is unique under arbitrary NGN topologies, compressor types, and sets of specifications. For GF setups where pressure is specified on a single (reference) node and compressors do no appear in cycles, the GF task is posed as an convex minimization. To handle more general setups, a GF solver relying on a mixed-integer quadratically-constrained quadratic program (MI-QCQP) is also devised. This solver can be used for any GF setup at any NGN. It introduces binary variables to capture flow directions; relaxes the pressure drop equations to quadratic inequality constraints; and uses a carefully selected objective to promote the exactness of this relaxation. The relaxation is provably exact in NGNs with non-overlapping cycles and a single fixed-pressure node. The solver handles efficiently the involved bilinear terms through McCormick linearization. Numerical tests validate our claims, demonstrate that the MI-QCQP solver scales well, and that the relaxation is exact even when the sufficient conditions are violated, such as in NGNs with overlapping cycles and multiple fixed-pressure nodes.

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arXiv2019

Designing reactive power control rules for smart inverters using support vector machines

Smart inverters have been advocated as a fast-responding mechanism for voltage regulation in distribution grids. Nevertheless, optimal inverter coordination can be computationally demanding, and preset local control rules are known to be subpar. Leveraging tools from machine learning, the design of customized inverter control rules is posed here as a multi-task learning problem. Each inverter control rule is modeled as a possibly nonlinear function of local and/or remote control inputs. Given the electric coupling, the function outputs interact to yield the feeder voltage profile. Using an approximate grid model, inverter rules are designed jointly to minimize a voltage deviation objective based on anticipated load and solar generation scenarios. Each control rule is described by a set of coefficients, one for each training scenario. To reduce the communication overhead between the grid operator and the inverters, we devise a voltage regulation objective that is shown to promote parsimonious descriptions for inverter control rules. Numerical tests using real-world data on a benchmark feeder demonstrate the advantages of the novel nonlinear rules and explore the trade-off between voltage regulation and sparsity in rule descriptions.

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arXiv2019

Optimal Scheduling of Water Distribution Systems

With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as energy storage alternatives if properly operated. Nevertheless, optimal WDS scheduling is challenged by the hydraulic law, according to which the pressure along a pipe drops proportionally to its squared water flow. The optimal water flow (OWF) task is formulated here as a mixed-integer non-convex problem incorporating flow and pressure constraints, critical for the operation of fixed-speed pumps, tanks, reservoirs, and pipes. The hydraulic constraints of the OWF problem are subsequently relaxed to second-order cone constraints. To restore feasibility of the original non-convex constraints, a penalty term is appended to the objective of the relaxed OWF. The modified problem can be solved as a mixed-integer second-order cone program, which is analytically shown to yield WDS-feasible minimizers under certain sufficient conditions. Under these conditions, by suitably weighting the penalty term, the minimizers of the relaxed problem can attain arbitrarily small optimality gaps, thus providing OWF solutions. Numerical tests using real-world demands and prices on benchmark WDS demonstrate the relaxation to be exact even for setups where the sufficient conditions are not met.

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arXiv2019

Power Flow Solvers for Direct Current Networks

With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This work puts forth three approaches with complementary strengths towards coping with the PF task in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. The first approach relies on a monotone mapping. In the absence of constant-power generation, the related iterates converge to the high-voltage solution, if one exists. To handle generators operating in constant-power mode at any time, an alternative Z-bus method is studied. For bounded constant-power generation and demand, the analysis establishes the existence and uniqueness of a PF solution within a predefined ball. Moreover, the Z-bus updates converge to this solution. Third, an energy function approach shows that under limited constant-power demand, all PF solutions are local minima of a function. The derived conditions can be checked without knowing the system state. The applicability of the conditions and the performance of the algorithms are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.

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arXiv2019

Smart Inverter Grid Probing for Learning Loads: Part I - Identifiability Analysis

Distribution grids currently lack comprehensive real-time metering. Nevertheless, grid operators require precise knowledge of loads and renewable generation to accomplish any feeder optimization task. At the same time, new grid technologies, such as solar photovoltaics and energy storage units are interfaced via inverters with advanced sensing and actuation capabilities. In this context, this two-part work puts forth the idea of engaging power electronics to probe an electric grid and record its voltage response at actuated and metered buses, to infer non-metered loads. Probing can be accomplished by commanding inverters to momentarily perturb their power injections. Multiple probing actions can be induced within a few tens of seconds. In Part I, load inference via grid probing is formulated as an implicit nonlinear system identification task, which is shown to be topologically observable under certain conditions. The conditions can be readily checked upon solving a max-flow problem on a bipartite graph derived from the feeder topology and the placement of actuated and non-metered buses. The analysis holds for single- and multi-phase grids, radial or meshed, and applies to phasor or magnitude-only voltage data. The topological observability of distribution systems using smart meter or phasor data is cast and analyzed a special case.

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arXiv2019

Smart Inverter Grid Probing for Learning Loads: Part II - Probing Injection Design

This two-part work puts forth the idea of engaging power electronics to probe an electric grid to infer non-metered loads. Probing can be accomplished by commanding inverters to perturb their power injections and record the induced voltage response. Once a probing setup is deemed topologically observable by the tests of Part I, Part II provides a methodology for designing probing injections abiding by inverter and network constraints to improve load estimates. The task is challenging since system estimates depend on both probing injections and unknown loads in an implicit nonlinear fashion. The methodology first constructs a library of candidate probing vectors by sampling over the feasible set of inverter injections. Leveraging a linearized grid model and a robust approach, the candidate probing vectors violating voltage constraints for any anticipated load value are subsequently rejected. Among the qualified candidates, the design finally identifies the probing vectors yielding the most diverse system states. The probing task under noisy phasor and non-phasor data is tackled using a semidefinite-program (SDP) relaxation. Numerical tests using synthetic and real-world data on a benchmark feeder validate the conditions of Part I; the SDP-based solver; the importance of probing design; and the effects of probing duration and noise.

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arXiv2019

Designing Power Grid Topologies for Minimizing Network Disturbances: An Exact MILP Formulation

The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the $H_2$-norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial (tree) and meshed (loopy) topologies for new networks. Although the design task can be posed as a mixed-integer semidefinite program (MI-SDP), its performance does not scale well with network size. Using McCormick relaxation, the topology design problem can be reformulated as a mixed-integer linear program (MILP). To improve the computation time, graphical properties are exploited to provide tighter bounds on the continuous optimization variables. Numerical tests on the IEEE 39-bus feeder demonstrate the efficacy of the optimal topology in minimizing disturbances.

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arXiv2019

Inverter Probing for Power Distribution Network Topology Processing

Knowing the connectivity and line parameters of the underlying electric distribution network is a prerequisite for solving any grid optimization task. Although distribution grids lack observability and comprehensive metering, inverters with advanced cyber capabilities currently interface solar panels and energy storage devices to the grid. Smart inverters have been widely used for grid control and optimization, yet the fresh idea here is to engage them towards network topology inference. Being an electric circuit, a distribution grid can be intentionally probed by instantaneously perturbing inverter injections. Collecting and processing the incurred voltage deviations across nodes can potentially unveil the grid topology even without knowing loads. Using grid probing data and under an approximate grid model, the tasks of topology recovery and line status verification are posed respectively as non-convex estimation and detection problems. Leveraging the features of the Laplacian matrix of a tree graph, probing terminal nodes is analytically shown to be sufficient for exact topology recovery if voltage data are collected at all buses. The related non-convex problems are surrogated to convex ones, which are iteratively solved via closed-form updates based on the alternating direction method of multipliers and projected gradient descent. Numerical tests on benchmark feeders demonstrate that grid probing can yield line status error probabilities of 0.001 by probing 40% of the nodes.

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arXiv2018

Optimal Distribution System Restoration with Microgrids and Distributed Generators

Increasing emphasis on reliability and resiliency call for advanced distribution system restoration (DSR). The integration of grid sensors, remote controls, and distributed generators (DG) brings about exciting opportunities in DSR. In this context, this work considers the task of single-step restoration of a single phase power distribution system. Different from existing works, the devised restoration scheme achieves optimal formation of islands without heuristically pre-identifying reference buses. It further facilitates multiple DGs running within the same island, and establishes a coordination hierarchy in terms of their PV/PQ operation modes. Generators without black-start capability are guaranteed to remain connected to a black-start DG or a substation. The proposed scheme models remotely-controlled voltage regulators exactly, and integrates them in the restoration process. Numerical tests on a modified IEEE 37-bus feeder demonstrate that the proposed mixed-integer linear program (MILP) takes less than four seconds to handle random outages of 1-5 lines. The scalability of this novel MILP formulation can be attributed to the unique use of cycles and paths on the grid infrastructure graph; the McCormick linearization technique; and an approximate power flow model.

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arXiv2018

Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver

The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks with random gas injections indicate that the relaxation is exact even when the derived conditions are not met.

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arXiv2018

Kernel-Based Learning for Smart Inverter Control

Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local control rules are subpar, the approach of customized control rules designed in a quasi-static fashion features as a golden middle. Departing from affine control rules, this work puts forth non-linear inverter control policies. Drawing analogies to multi-task learning, reactive control is posed as a kernel-based regression task. Leveraging a linearized grid model and given anticipated data scenarios, inverter rules are jointly designed at the feeder level to minimize a convex combination of voltage deviations and ohmic losses via a linearly-constrained quadratic program. Numerical tests using real-world data on a benchmark feeder demonstrate that nonlinear control rules driven also by a few non-local readings can attain near-optimal performance.

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arXiv2018

Graph Algorithms for Topology Identification using Power Grid Probing

To perform any meaningful optimization task, power distribution operators need to know the topology and line impedances of their electric networks. Nevertheless, distribution grids currently lack a comprehensive metering infrastructure. Although smart inverters are widely used for control purposes, they have been recently advocated as the means for an active data acquisition paradigm: Reading the voltage deviations induced by intentionally perturbing inverter injections, the system operator can potentially recover the electric grid topology. Adopting inverter probing for feeder processing, a suite of graph-based topology identification algorithms is developed here. If the grid is probed at all leaf nodes but voltage data are metered at all nodes, the entire feeder topology can be successfully recovered. When voltage data are collected only at probing buses, the operator can find a reduced feeder featuring key properties and similarities to the actual feeder. To handle modeling inaccuracies and load non-stationarity, noisy probing data need to be preprocessed. If the suggested guidelines on the magnitude and duration of probing are followed, the recoverability guarantees carry over from the noiseless to the noisy setup with high probability.

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arXiv2018

Optimal Real-Time Coordination of Energy Storage Units as a Voltage-Constrained Game

With increasingly favorable economics and bundling of different grid services, energy storage systems (ESS) are expected to play a key role in integrating renewable generation. This work considers the coordination of ESS owned by customers located at different buses of a distribution grid. Customers participate in frequency regulation and experience energy prices that increase with the total demand. Charging decisions are coupled across time due to battery dynamics, as well as across network nodes due to competitive pricing and voltage regulation constraints. Maximizing the per-user economic benefit while maintaining voltage magnitudes within allowable limits is posed here as a network-constrained game. It is analytically shown that a generalized Nash equilibrium exists and can be expressed as the minimizer of a convex yet infinite-time horizon aggregate optimization problem. To obtain a practical solution, a Lyapunov optimization approach is adopted to design a real-time scheme offering feasible charging decisions with performance guarantees. The proposed method improves over the standard Lyapunov technique via a novel weighting of user costs. By judiciously exploiting the physical grid response, a distributed implementation of the real-time solver is also designed. The features of the novel algorithmic designs are validated using numerical tests on realistic datasets.

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arXiv2017

PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches

This chapter aspires to glean some of the recent advances in power system state estimation (PSSE), though our collection is not exhaustive by any means. The Cram{é}r-Rao bound, a lower bound on the (co)variance of any unbiased estimator, is first derived for the PSSE setup. After reviewing the classical Gauss-Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. A disciplined paradigm for distributed and decentralized schemes is subsequently exemplified under linear(ized) and exact grid models. Novel bad data processing models and fresh perspectives linking critical measurements to cyber-attacks on the state estimator are presented. Finally, spurred by advances in online convex optimization, model-free and model-based state trackers are reviewed.

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arXiv2017

Voltage Analytics for Power Distribution Network Topology Verification

Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling. While synchrophasor installations are limited in low-voltage grids, utilities have an abundance of smart meter data at their disposal. In this context, a statistical learning framework is put forth for verifying single-phase grid structures using non-synchronized voltage data. The related maximum likelihood task boils down to minimizing a non-convex function over a non-convex set. The function involves the sample voltage covariance matrix and the feasible set is relaxed to its convex hull. Asymptotically in the number of data, the actual topology yields the global minimizer of the original and the relaxed problems. Under a simplified data model, the function turns out to be convex, thus offering optimality guarantees. Prior information on line statuses is also incorporated via a maximum a-posteriori approach. The formulated tasks are tackled using solvers having complementary strengths. Numerical tests using real data on benchmark feeders demonstrate that reliable topology estimates can be acquired even with a few smart meter data, while the non-convex schemes exhibit superior line verification performance at the expense of additional computational time.

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arXiv2016

Enhancing Observability in Distribution Grids using Smart Meter Data

Due to limited metering infrastructure, distribution grids are currently challenged by observability issues. On the other hand, smart meter data, including local voltage magnitudes and power injections, are communicated to the utility operator from grid buses with renewable generation and demand-response programs. This work employs grid data from metered buses towards inferring the underlying grid state. To this end, a coupled formulation of the power flow problem (CPF) is put forth. Exploiting the high variability of injections at metered buses, the controllability of solar inverters, and the relative time-invariance of conventional loads, the idea is to solve the non-linear power flow equations jointly over consecutive time instants. An intuitive and easily verifiable rule pertaining to the locations of metered and non-metered buses on the physical grid is shown to be a necessary and sufficient criterion for local observability in radial networks. To account for noisy smart meter readings, a coupled power system state estimation (CPSSE) problem is further developed. Both CPF and CPSSE tasks are tackled via augmented semi-definite program relaxations. The observability criterion along with the CPF and CPSSE solvers are numerically corroborated using synthetic and actual solar generation and load data on the IEEE 34-bus benchmark feeder.

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arXiv2016

Two-Timescale Stochastic Dispatch of Smart Distribution Grids

Smart distribution grids should efficiently integrate stochastic renewable resources while effecting voltage regulation. The design of energy management schemes is challenging, one of the reasons being that energy management is a multistage problem where decisions are not all made at the same timescale and must account for the variability during real-time operation. The joint dispatch of slow- and fast-timescale controls in a smart distribution grid is considered here. The substation voltage, the energy exchanged with a main grid, and the generation schedules for small diesel generators have to be decided on a slow timescale; whereas optimal photovoltaic inverter setpoints are found on a more frequent basis. While inverter and looser voltage regulation limits are imposed at all times, tighter bus voltage constraints are enforced on the average or in probability, thus enabling more efficient renewable integration. Upon reformulating the two-stage grid dispatch as a stochastic convex-concave problem, two distribution-free schemes are put forth. An average dispatch algorithm converges provably to the optimal two-stage decisions via a sequence of convex quadratic programs. Its non-convex probabilistic alternative entails solving two slightly different convex problems and is numerically shown to converge. Numerical tests on a real-world distribution feeder verify that both novel data-driven schemes yield lower costs over competing alternatives.

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