A Linear AC-OPF Formulation for Unbalanced Distribution Networks

Giraldo, Juan S.; Vergara, Pedro P.; López, Juan Camilo; Nguyen, Phuong H.; Paterakis, Nikolaos G.

doi:10.1109/tia.2021.3085799

Cited by 21 publications

(11 citation statements)

References 33 publications

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“…In ( 4) and ( 5), the real and imaginary current of the phases is calculated. Te neutral wire current of the lines is also calculated in (7). Finally, the zero-point voltage of the distribution substation is expressed in (8).…”

Section: Power Flowmentioning

confidence: 99%

“…Four diferent objects need to be optimized in this scheme, including the expected operating cost of the microgrids, expected pollutant amount, expected energy not-supplied, and voltage deviation. A new solution to AC optimal power fow in unbalanced networks is suggested in [7] so that the energy generation cost is minimized and the voltage and current of the network are maintained within the permissible limits. Reference [8] presents a two-stage optimal operation method for a network, in which various uncertain parameters related to demand are taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Operation of Distributed Generations in Four-Wire Unbalanced Distribution Systems considering Different Models of Loads

Jin

Moradi

Rashidi

2023

International Transactions on Electrical Energy Systems

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The distribution network is generally unbalanced due to the distribution of consumers in different phases and the different status of their energy consumption. Also, in recent years, the utilization of distributed generations (DGs) has flourished in the distribution network, thanks to their favorable operational and environmental benefits. Therefore, it is predicted that the optimal energy management of DGs in the unbalanced distribution network can improve the operation state of the network. Moreover, the consumer load model is generally a combination of constant impedance, constant current, and constant power conditions. Therefore, the current study focuses on the analysis of the operation of unbalanced four-wire distribution systems containing DGs, in which load models are also involved. An optimization structure is established to make the voltage deviation, power loss, neutral wire loss, and voltage unbalance minimized. Limitations of the problem include those related to the network and those concerning operating indices of the system like voltage magnitude and phase angle of buses, power flow through the distribution lines, constraints of operation of DGs, load model, and unbalanced conditions. The problem formed in this study is nonlinear and is solved using sequential quadratic programming (SQP) by implementing it in the GAMS simulation environment. To test the benefits of the introduced approach, a 13-bus distribution system has been adopted so that the optimal operation of DGs in the distribution network has been able to reduce the unbalanced situation of the network compared to the power flow studies. Also, this scheme has improved the operation of network, where energy losses and voltage drop have been reduced compared to power flow studies, and a smooth voltage profile has been extracted.

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Section: Power Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Operation of Distributed Generations in Four-Wire Unbalanced Distribution Systems considering Different Models of Loads

Jin

Moradi

Rashidi

2023

International Transactions on Electrical Energy Systems

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“…where η = 2/(1 + 4 -2 2 ); X + = max{|x re ||x im |}; and X -= min{|x re ||x im |}. Thus, (34) can be extended to estimate the square of current magnitude as [34], [36]:…”

Section: B Milp Problem Formulationmentioning

confidence: 99%

A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

Vergara

Giraldo

Salazar

et al. 2023

Journal of Modern Power Systems and Clean Energy

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A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.

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“…The last step towards a complete single-period OPF model is handling the non-convex constraint (5c) and the left part of (1f). As in [10], [11], the bilinear constraint (5c) is convexified by replacing the real and imaginary parts of voltage phasors with fixed parameters (e.g. an initialization of voltage phasors with 1 per-unit (pu) magnitude and 120°difference between phases), shown in (11).…”

Section: Convexification and Solution Approachmentioning

confidence: 99%

“…Fig. 2 shows the derivation of the convex envelope for the phase a. Voltage angle limits are first imposed on the non-convex feasible region in (a), leading to a reduced feasible region of (b), which is justified by the small voltage angle deviation for distribution networks [10]. Following this, the convex envelope of the feasible region in (b) is derived, shown in (c).…”

Section: Convexification and Solution Approachmentioning

confidence: 99%

Managing Distributed Energy Resources with Intertemporal Characteristics in Low-voltage Power Grids: A Single-period OPF Approach

Zhan¹,

Morren²,

Akker³

et al. 2022

Preprint

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A Linear AC-OPF Formulation for Unbalanced Distribution Networks

Cited by 21 publications

References 33 publications

Optimal Operation of Distributed Generations in Four-Wire Unbalanced Distribution Systems considering Different Models of Loads

Optimal Operation of Distributed Generations in Four-Wire Unbalanced Distribution Systems considering Different Models of Loads

A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

Managing Distributed Energy Resources with Intertemporal Characteristics in Low-voltage Power Grids: A Single-period OPF Approach

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