On reactive power flow and voltage stability in microgrids

Gentile, B. De; Simpson-Porco, John W.; Dörfler, Florian; Zampieri, Sandro; Bullo, Francesco

doi:10.1109/acc.2014.6859434

Cited by 25 publications

(32 citation statements)

References 20 publications

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“…The first two terms in (41a) are the approximate solution for decoupled reactive power flow, as obtained in [13], [26]. The third term is novel, and captures how -to lowest order -active power injections affect voltage magnitudes quadratically.…”

Section: G Approximate Solution To Lossless Power Flowmentioning

confidence: 99%

A Theory of Solvability for Lossless Power Flow Equations—Part I: Fixed-Point Power Flow

Simpson-Porco¹

2018

IEEE Trans. Control Netw. Syst.

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Abstract-This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is stated for both meshed and radial networks, and is parameterized by several graph-theoretic matrices -the power network stiffness matrices -which quantify the internal coupling strength of the network. The model leads immediately to an explicit approximation of the high-voltage power flow solution. For standard test cases, we find that iterates of the fixedpoint power flow converge rapidly to the high-voltage power flow solution, with the approximate solution yielding accurate predictions near base case loading. In Part II, we leverage the fixed-point power flow to study power flow solvability, and for radial networks we derive conditions guaranteeing the existence and uniqueness of a high-voltage power flow solution. These conditions (i) imply exponential convergence of the fixed-point power flow iteration, and (ii) properly generalize the textbook two-bus system results.Index Terms-Power flow equations, complex networks, power systems, circuit theory, optimal power flow, fixed point theorems. I . I N T R O D U C T I O NThe power flow equations describe the balance and flow of power in a synchronous AC power system. The solutions of these equations (also called operating points of the network) describe the configurations of voltages and currents which (i) are physically consistent with Kichhoff's and Ohm's laws, and (ii) meet the prescribed boundary conditions, specified in terms of fixed power injections or fixed voltage levels at particular nodes in the network. Knowledge of the current system operating point is crucial, as is understanding how the current operating point will change as control actions are taken or as unexpected contingencies occur. As such, the power flow equations are embedded in nearly every power system analysis or control problem, including optimal power flow and its security-constrained variants, transient and voltage stability assessment, contingency screening, short-circuit analysis, and wide-area monitoring/control [1].As the equations are nonlinear, the existence of real-valued solutions is not guaranteed: lightly loaded networks typically possess many solutions [2], while a network which is loaded sufficiently will possess none. Despite this potential for both multiple reasonable solutions and infeasibility, typically there is a single desirable solution, characterized by high voltage magnitudes at buses and small inter-bus current flows. This solution is often termed stable, as it behaves in a manner Aside from intellectual merit, there are at least two important engineering motivations for understanding solvability. The first is to better understand the convergence of iterative numerical algorithms for solving power flow equations. When a power flow solver diverges, it may be because of a numerical instability in the algorithm, an ini...

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Section: G Approximate Solution To Lossless Power Flowmentioning

confidence: 99%

A Theory of Solvability for Lossless Power Flow Equations—Part I: Fixed-Point Power Flow

Simpson-Porco¹

2018

IEEE Trans. Control Netw. Syst.

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“…In our initial setup, we assumed constant current or constant impedance loads, and we considered purely resistive networks or networks with lines modeled by the resistive-capacitive Π-model. In ongoing and future work, we plan to study the robust performance in presence of transient stochastic disturbances as well as different network models including resistive-inductive-capacitive lines and constant power load models using the approximation proposed in Gentile, Simpson-Porco, Dörfler, Zampieri, and Bullo (2014).…”

Section: Discussionmentioning

confidence: 99%

Distributed control and optimization in DC microgrids

2015

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“…which equals the DC power flow model [11] for the active power and a corresponding linear DC model for the reactive power and voltage [12]:…”

Section: Linearization Around the Flat Voltage Solutionmentioning

confidence: 99%

“…In Section III we show how an implicit linear approximation for the power flow manifold can be obtained via geometric methods. We also illustrate how the proposed model generalizes all standard linear power flow models, including polar/rectangular DC power flow and their variations [8]- [12] as well as LinDistFlow [13]- [15], how to assess and improve its approximation accuracy, and how to extend it to three-phase networks. In Section IV we show how to use the approximation of the power flow manifold to solve a power flow analysis problem, where bus loads are introduced (the MatLab/GNU Octave code is available in a public online repository [16]).…”

Section: Introductionmentioning

confidence: 98%

Fast power system analysis via implicit linearization of the power flow manifold

Bolognani

Dörfler

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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125

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In this paper, we consider the manifold that describes all feasible power flows in a power system as an implicit algebraic relation between nodal voltages (in polar coordinates) and nodal power injections (in rectangular coordinates). We derive the best linear approximant of such a relation around a generic solution of the power flow equations. Our linear approximant is sparse, computationally attractive, and preserves the structure of the power flow. Thanks to the full generality of this approach, the proposed linear implicit model can be used to obtain a fast approximate solution of a possibly unbalanced three phase power system, with either radial or meshed topology, and with general bus models. We demonstrate how our approximant includes standard existing linearizations, we validate the quality of the approximation via simulations on a standard testbed, and we illustrate its applicability with case studies in scenario-based optimization and cascading failures.

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On reactive power flow and voltage stability in microgrids

Cited by 25 publications

References 20 publications

A Theory of Solvability for Lossless Power Flow Equations—Part I: Fixed-Point Power Flow

A Theory of Solvability for Lossless Power Flow Equations—Part I: Fixed-Point Power Flow

Distributed control and optimization in DC microgrids

Fast power system analysis via implicit linearization of the power flow manifold

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