ACOPF for three‐phase four‐conductor distribution systems: semidefinite programming based relaxation with variable reduction and feasible solution recovery

Liu, Yikui; Li, Jie; Wu, Lei

doi:10.1049/iet-gtd.2018.5033

Cited by 15 publications

(19 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Z kr l is a transformation of Z l , directly linking the voltage drop in the phase conductors to only the current in the phase conductors [25]. Rewriting (14) and substituting it in the definition of S lij [P] and S lji [P], leads to a non-linear constraint linking these variables directly to U i and U j ,…”

Section: E Linesmentioning

confidence: 99%

See 1 more Smart Citation

Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

Claeys

Geth

2021

IEEE Trans. Smart Grid

View full text Add to dashboard Cite

Mathematical models representing the behavior of electrical loads are an important part of any optimal power flow problem. The current state-of-the-art in unbalanced optimal power flow mostly considers wye-connected, constant power loads. However, for applications such as conservation voltage reduction, it is crucial to model how the consumption of the loads depends on the voltage of the network. This article develops a unified framework to handle a wide variety of load types: delta-or wye-connected, constant power, constant current and exponential load models. Furthermore, it proposes a novel convex relaxation for the exponential model, using power cones, that is intersected next with a well-known semi-definite relaxation of unbalanced OPF. Finally, numerical results on the LVTestCase feeder are included for both the exact, non-linear equations and the convex relaxation, which show how considering the voltage sensitivity and connection type can lead to different objective values and voltage profiles. Additional results for 128 low-voltage networks, examine the quality of the solutions obtained with the proposed relaxation.

show abstract

Section: E Linesmentioning

confidence: 99%

“…Wei et al solve a sequence of convexified penalization problems [13]. Liu et al propose a method to recover a feasible solution when the relaxation is inexact [14]. Convex relaxations also play an important role AND β (REACTIVE POWER), BY DEVICE TYPE [10] in approaches for global optimization of the non-linear OPF problem [15].…”

Section: Introductionmentioning

confidence: 99%

Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

Claeys

Geth

2021

IEEE Trans. Smart Grid

View full text Add to dashboard Cite

show abstract

“…Similarly, (9) and (10) represent the three-phase active and reactive power from each DG unit. Expressions relating active and reactive power from loads are shown in (11) and (12), respectively. Operational limits regarding the capability curve of DG units are considered in (7) and (8), while nodal voltage and branch magnitude limits are considered in (14) and (13), respectively.…”

Section: Minlp Optimal Power Flowmentioning

confidence: 99%

A Novel Linear Optimal Power Flow Model for Three-Phase Electrical Distribution Systems

Giraldo¹,

Vergara²,

López³

et al. 2020

Preprint

View full text Add to dashboard Cite

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L∞ norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4\% for currents and 0.005\% for voltages.

show abstract

“…Especially for large scale grids, it can be challenging to solve the TOPF problem if it is formulated as a single optimization problem [28]. Therefore, simplification techniques are presented in literature, for example linearization ( [20,23,27]), relaxation and convexification techniques ( [21,[29][30][31]) and distributed [32] or stochastical approaches [19].…”

Section: Introductionmentioning

confidence: 99%

An Optimal Power Flow Algorithm for the Simulation of Energy Storage Systems in Unbalanced Three-Phase Distribution Grids

et al. 2021

View full text Add to dashboard Cite

An optimal power flow algorithm for unbalanced three-phase distribution grids is presented in this paper as a new tool for grid planning on low voltage level. As additional equipment like electric vehicles, heat pumps or solar power systems can sometimes cause unbalanced power flows, existing algorithms have to be adapted. In comparison to algorithms considering balanced power flows, the presented algorithm uses a complete model of a three-phase four-wire low voltage grid. Additionally, a constraint for the voltage unbalance in the grid is introduced. The algorithm can be used to optimize the operation of energy storage systems in unbalanced systems. The used grid model, constraints, objective function and solver are explained in detail. A validation of the algorithm using a commercial tool is done. Additionally, three exemplary optimizations are performed to show possible applications for this tool.

show abstract

ACOPF for three‐phase four‐conductor distribution systems: semidefinite programming based relaxation with variable reduction and feasible solution recovery

Cited by 15 publications

References 28 publications

Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

Voltage-Dependent Load Models in Unbalanced Optimal Power Flow Using Power Cones

A Novel Linear Optimal Power Flow Model for Three-Phase Electrical Distribution Systems

An Optimal Power Flow Algorithm for the Simulation of Energy Storage Systems in Unbalanced Three-Phase Distribution Grids

Contact Info

Product

Resources

About