A Condition of Equivalence Between Bus Injection and Branch Flow Models in Radial Networks

Ding, Tao; Lu, Runzhao; Yang, Yongheng; Blaabjerg, Frede

doi:10.1109/tcsii.2019.2916208

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…An alternative formulation can be implemented by taking advantage of the sparsity in the incidence matrix of radial networks. The Bus Injection Model (BIM) considers the current flow through each line (sending and receiving flows) connected to the node, as can be observed in Equation (2) [37]. This formulation continues being nonconvex.…”

Section: Ac-opf Formulationsmentioning

confidence: 99%

Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function

Osorio

Rosero

2023

Energies

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This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.

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Section: Ac-opf Formulationsmentioning

confidence: 99%

Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function

Osorio

Rosero

2023

Energies

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“…There exist two main declinations of the AC OPF problem: the Bus Injection Model (BIM), and the Branch Flow Model (BFM), both presented in [1]. Both formulations are equivalent for radial connected networks [2]. In this paper, we choose the BFM formulation since it makes our arguments easier to present.…”

Section: Optimal Power Flow Problemmentioning

confidence: 99%

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

Grangereau

Ackooij

Gaubert

2022

Electric Power Systems Research

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We propose a generic multistage stochastic model for the Alternating Current Optimal Power Flow (AC OPF) problem for radial distribution networks, to account for the random electricity production of renewable energy sources and dynamic constraints of storage systems. We consider single-phase radial networks. Radial three-phase balanced networks (medium-voltage distribution networks typically have this structure) reduce to the former case. This induces a large scale optimization problem, which, given the non-convex nature of the AC OPF, is generally challenging to solve to global optimality.We derive a priori conditions guaranteeing a vanishing relaxation gap for the multi-stage AC OPF problem, which can thus be solved using convex optimization algorithms. We also give an a posteriori upper bound on the relaxation gap. In particular, we show that a null or low relaxation gap may be expected for applications with light reverse power flows or if sufficient storage capacities with low cost are available. Then, we discuss the validity of our results when incorporating voltage regulation devices. Finally, we illustrate our results on problems of planning of a realistic distribution feeder with distributed solar production and storage systems. Scenario trees for solar production

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“…Alternating current power flow (ACPF) is a general PF model which has a full consideration of system parameters. However, due to its complexity and non-convexity [6], ACPF cannot be applied directly. The Distflow model, as a simplification of ACPF for radial distribution systems is proposed by [7], assuming zero line shunts.…”

Section: Introductionmentioning

confidence: 99%

A Linear Distflow Model Considering Line Shunts

Lin¹,

Shen²,

Ye³

et al. 2023

Preprint

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<p>Line shunts are usually ignored by various power flow (PF) models in distribution system analysis, planning and optimization. However, ``charging effects" from line shunts of underground/submarine power cables would cause non-negligible model errors for these commonly used PF models. In this brief, we propose a modified linear Distflow model (LinDist) with line shunts (LinDistS) to address relevant model errors. The strength of the proposed model not only lies in a straightforward structure like LinDist, but also maintaining the linearity after further considering three-phase unbalanced systems. The linearization error of voltage component is theoretically analyzed. Case studies show that compared with non-linear and linear models, LinDistS achieves the descent calculation accuracy and efficiency in large scale distribution systems.</p>

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A Condition of Equivalence Between Bus Injection and Branch Flow Models in Radial Networks

Cited by 7 publications

References 27 publications

Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function

Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function

Multi-stage Stochastic Alternating Current Optimal Power Flow with Storage: Bounding the Relaxation Gap

A Linear Distflow Model Considering Line Shunts

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