High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms

Dvijotham, Krishnamurthy; Mallada, Enrique; Simpson-Porco, John W.

doi:10.1109/lcsys.2017.2717578

Cited by 26 publications

(11 citation statements)

References 24 publications

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“…The theorems certify the existence of a maximum equilibrium α ∈ R n >0 such that α ≥ r * for all r * ∈ M. In addition, α is asymptotically stable as long as the Jacobian of ( 6) is nonsingular at α. The same result for power flow equations (i.e., the existence of a stable high-voltage power flow solution) has been obtained in recent papers [20], [21], along with algorithm that provably finds the solution.…”

Section: Characterization Of Roasupporting

confidence: 71%

Novel Region of Attraction Characterization for Control and Stabilization of Voltage Dynamics

Cui¹,

Zamzam²,

Bernstein³

2020

Preprint

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In this paper, we study the monitoring and control of long-term voltage stability considering load tap-changer (LTC) dynamics. We show that under generic conditions, the LTC dynamics always admit a unique stable equilibrium. For the stable equilibrium, we characterize an explicit inner approximation of its region of attraction (ROA). Compared to existing results, the computational complexity of the ROA characterization is drastically reduced. A quadratically constrained linear program formulation for the ROA characterization problem is proposed. In addition, we formulate a second-order cone program for online voltage stability monitoring and control exploiting the proposed ROA characterization, along with an ADMM-based distributed algorithm to solve the problem. The efficacy of the proposed formulations and algorithms is demonstrated using a standard IEEE test system.

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Section: Characterization Of Roasupporting

confidence: 71%

Novel Region of Attraction Characterization for Control and Stabilization of Voltage Dynamics

Cui¹,

Zamzam²,

Bernstein³

2020

Preprint

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“…x kl for all pk , kl ∈ E. This assumption is reasonable in distribution networks because in most networks the resistances are decreasing as we move away from the feeder since the power losses should be kept small. Similar assumptions are made in Dvijotham et al (2017) and Low (2014b).…”

Section: Continuity Of the Optimal Allocation Functionmentioning

confidence: 93%

“…This result is needed in Section 5 to show convergence of the fluid-scaled processes. Last, in power system analysis, rigorous proofs are typically difficult and require additional assumptions on the distribution system (Dvijotham et al 2017), even if one ignores the stochastic dynamics. In the rest of this section, we make an additional assumption for the ratio of resistance and reactance.…”

Section: Continuity Of the Optimal Allocation Functionmentioning

confidence: 99%

A Fluid Model of an Electric Vehicle Charging Network

2022

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We develop and analyze a measure-valued fluid model keeping track of parking and charging requirements of electric vehicles in a local distribution grid. We show how this model arises as an accumulation point of an appropriately scaled sequence of stochastic network models. Our analysis incorporates load-flow models that describe the laws of electricity. Specifically, we consider the alternating current (AC) and the linearized Distflow power flow models and show a continuity property of the associated power allocation functions.

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“…Historically used for stability analysis, the energy function minimization technique has been recently geared towards the PF task in AC systems [20], but the conditions ensuring convexity of the energy function depend on the sought system state. The energy function proposed in [18] is shown to be convex at all PF solutions in AC networks with constant resistance-to-reactance ratios.…”

Section: Introductionmentioning

confidence: 98%

Power Flow Solvers for Direct Current Networks

Taheri

Kekatos

2020

IEEE Trans. Smart Grid

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With increasing direct current (DC) deployments in distribution feeders, microgrids, smart buildings, and highvoltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions and 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 PF solution, if one exists. To handle distributed renewable generators typically operating in constantpower mode, 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 minimization approach shows that under limited constant-power demand, all PF solutions are locally stable. The derived conditions can be readily checked without knowing the system state. The applicability of the conditions and the performance of the iterative schemes are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.

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High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms

Cited by 26 publications

References 24 publications

Novel Region of Attraction Characterization for Control and Stabilization of Voltage Dynamics

Novel Region of Attraction Characterization for Control and Stabilization of Voltage Dynamics

A Fluid Model of an Electric Vehicle Charging Network

Power Flow Solvers for Direct Current Networks

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