Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations

Leveringhaus, Thomas; Breithaupt, Timo; Garske, Steffen; Hofmann, Lutz

doi:10.1109/powercon.2018.8601613

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…Equality constraints in (22) are the classical non-linear real and reactive power balance equations for all AC and DC nodes indistinctly. It is noted that for the DC grid, the reactive power balance results in a value of zero since the reactive injections to the DC grid are controlled by the variable B eq in conjunction with the "Zero Constraint" given in (24). Thus, for a specified number of generation units to satisfy a particular pattern of load per bus, the complex power balance equations of the system using FUBM are given by (31) [20].…”

Section: Flexible Opf Formulation Using Fubmmentioning

confidence: 99%

“…Moreover, any solution for a hybrid network should be able to properly reflect the intricacies of the converters' interactions and capture enough detail to be a realistic representation of the actual system. Existing solution methods normally employ a sequential method for solving the AC and DC parts of a hybrid network in sequence [24,25,26]. As a result, the equations per model and grid vary accordingly.…”

Section: Introductionmentioning

confidence: 99%

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Universal branch model for the solution of optimal power flows in hybrid AC/DC grids

Alvarez-Bustos

Kazemtabrizi

Shahbazi

et al. 2021

International Journal of Electrical Power & Energy Systems

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This paper presents a universal model formulation for solving Optimal Power Flows for hybrid AC/DC grids. The prowess of the new formulation is that it (i) provides a direct link between AC and DC parts of the grid allowing for solving the entire network within a unified frame of reference (not sequentially) and (ii) can realistically model any element within the AC/DC power grid, ranging from conventional AC transmission lines to multiple types of AC/DC interface devices such as Voltage Source Converters (VSC) by introducing additional control variables. The model is formulated in such a way that it does not make a distinction, from a mathematical perspective, between AC and DC elements and the ensuing optimal power flow (OPF) problem can be solved via model-based optimization solvers as a mathematical programming problem. Simulations carried out using a variety of non-linear gradient-based solvers in AIMMS © on a small contrived and a large realistic test system (modified PEGASE) clearly show that the universal model is on par with existing methodologies for solving OPFs both in accuracy of the solution and computational e ciency. Meanwhile, simulations carried out on a series of AC and AC/DC test systems show that the model is scalable and stays computationally tractable for larger system sizes without sacrificing convergence time. Reactive Power Q t Constraint v f Voltage "from" g P v dp Voltage Droop Constraint v t Voltage "to" g G sw VSC losses correction Constraint i f Current "from" h S 2 f Loadability Constraint "from" i t Current "to" h S 2 t Loadability Constraint "to" S f Complex Power "from" L S 2 L

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Section: Flexible Opf Formulation Using Fubmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Universal branch model for the solution of optimal power flows in hybrid AC/DC grids

Alvarez-Bustos

Kazemtabrizi

Shahbazi

et al. 2021

International Journal of Electrical Power & Energy Systems

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“…Therefore, this paper presents the comparison of two, independently developed optimization methods (see section 3) for the solution of the SCOPF problem described in section 2. The first approach is a solution by a sequentially solved convexificated Quadratically Constrained Quadratic Program (SQCQP) based on [5][6][7][8], which is presented in section 3.1. The second approach solves a mixed integer, non-linear optimization problem using a modified particle swarm optimization (PSO) e.g.…”

Section: Motivationmentioning

confidence: 99%

“…The first approach applies a sequentially solved novel convexificated Quadratically Constrained Quadratic Program (SQCQP) based on [5][6][7][8] that is further developed in this paper to consider in-phase and quadrature voltage controlled transformers. For the convexification, the equations of the SCOPF need to be reformulated as real-valued system of equations with equal number of equations and variables and a maximal polynomial degree of two.…”

Section: Sqcqp Approachmentioning

confidence: 99%

Comparison of Convexificated SQCQP and PSO for the Optimal Transmission System Operation based on Incremental In-Phase and Quadrature Voltage Controlled Transformers

Sarstedt,

Leveringhaus,

Kluß

et al. 2021

Preprint

Self Cite

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The optimal operation of electrical energy systems by solving a security constrained optimal power flow (SCOPF) problem is still a challenging research aspect. Especially, for conventional optimization methods like sequential quadratic constrained quadratic programming (SQCQP) the formulation of the incremental control variables like in-phase and quadrature voltage controlled transformers in a solver suitable way is complex. Compared to this, the implementation of these control variables within heuristic approaches like the particle swarm optimization (PSO) is simple but problem specific adaptations of the classic PSO algorithm are necessary to avoid an unfortunate swarm behavior and local convergence in bad results. The objective of this paper is to introduce a SQCQP and a modified PSO approach in detail to solve the SCOPF problem adequately under consideration of flexible incremental in-phase and quadrature transformers tap sets and to compare and benchmark the results of both approaches for an adapted IEEE 118-bus system. The casestudy shows that both approaches lead to suitable results of the SCOPF with individual advantages of the SQCQP concerning the quality and the reproducibility of the results while the PSO lead to faster solutions when the complexity of the investigation scenario increases.

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Detailed reasoning and derivation of a convexificated quadratic approximation approach for the Security Constrained Optimal Power Flow

Leveringhaus

Hofmann

2020

2020 International Conference on Smart Grids and Energy Systems (SGES)

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Modelling of Sequential Optimal Power Flow by Piecewise Linear Convexificated Quadratic Approximations

Cited by 5 publications

References 6 publications

Universal branch model for the solution of optimal power flows in hybrid AC/DC grids

Universal branch model for the solution of optimal power flows in hybrid AC/DC grids

Comparison of Convexificated SQCQP and PSO for the Optimal Transmission System Operation based on Incremental In-Phase and Quadrature Voltage Controlled Transformers

Detailed reasoning and derivation of a convexificated quadratic approximation approach for the Security Constrained Optimal Power Flow

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