Linear/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations

Fortenbacher, Philipp; Demiray, Turhan

doi:10.1016/j.ijepes.2018.12.008

Cited by 76 publications

(42 citation statements)

References 36 publications

(67 reference statements)

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“…We mainly use the linear power and branch flow approximation presented in [4]. Here, we summarize the main results, for full details see [4].…”

Section: Methodsmentioning

confidence: 99%

“…We mainly use the linear power and branch flow approximation presented in [4]. Here, we summarize the main results, for full details see [4]. As an extension, we derive transfer distribution factors (TDFs) for voltage magnitudes (VTDF), angles (θTDF) and active /reactive power branch flows (PTDF) as a function of the nodal active and reactive power.…”

Section: Methodsmentioning

confidence: 99%

“…In contrast to this, we developed a method that does not require the search of supporting points and the solutions of multiple OPF problems. Instead, we use linear power flow approximations [4] to compute a polytope that defines the PQ capability area, which reduces the computational complexity significantly. As another advantage, our formulation could be directly incorporated as linear constraints in OPF problems to represent distribution grids.…”

Section: Related Work and Contributionmentioning

confidence: 99%

“…As derived in [4] the lossless power flow approximation in a network with n b buses and n l branches is…”

Section: Linear Power Flow Approximationmentioning

confidence: 99%

“…In accordance with [4] and with the θTDF and VTDF matrix, we can express the branch flow active and reactive powers p f , q f ∈ R n l ×1 as…”

Section: Linear Branch Flow Approximationmentioning

confidence: 99%

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Reduced and aggregated distribution grid representations approximated by polyhedral sets

Fortenbacher

Demiray

2020

International Journal of Electrical Power & Energy Systems

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In this paper we present a novel tractable method to compute reduced and aggregated distribution grid representations that provide an interface in the form of active and reactive power (PQ) capability areas for improving transmission service operator -distribution service operator (TSO-DSO) interactions. Based on a lossless linear power flow approximation we derive polyhedral sets to determine a reduced PQ operating region capturing all voltage magnitude and branch power flow constraints of the entire distribution grid. To demonstrate the usefulness of our method, we compare the capability area obtained from the polyhedral approximation with an area generated by multiple optimal power flow (OPF) solutions for different distribution grids. While the approximation errors are reasonable, especially for low voltage (LV) grids, the computational complexity to compute the PQ capability area can be significantly reduced with our proposed method.

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“…We mainly use the linear power and branch flow approximation presented in [4]. Here, we summarize the main results, for full details see [4].…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Related Work and Contributionmentioning

confidence: 99%

“…As derived in [4] the lossless power flow approximation in a network with n b buses and n l branches is…”

Section: Linear Power Flow Approximationmentioning

confidence: 99%

“…In accordance with [4] and with the θTDF and VTDF matrix, we can express the branch flow active and reactive powers p f , q f ∈ R n l ×1 as…”

Section: Linear Branch Flow Approximationmentioning

confidence: 99%

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Reduced and aggregated distribution grid representations approximated by polyhedral sets

Fortenbacher

Demiray

2020

International Journal of Electrical Power & Energy Systems

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Hybrid renewable/nonrenewable/storage resources in electrical grid considering active‐reactive losses and depth of discharge

Hemmati

Mahdavi

2021

Int J Energy Res

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This paper presents a linear model for optimal operation of distributed generations (DGs) including renewable and nonrenewable DGs in the electrical grids.The accurate model of active-reactive losses is formed by two quadratic terms that are linearized by piecewise linear approximation of the quadratic curves.The DGs' technical/economic formulations are also presented based on the linear model. The proposed linear models are combined to implement linear optimal power flow (OPF) in the electrical grid integrated with hybrid diesel/wind/ solar/battery. The model is associated with uncertainties and expressed as stochastic mixed integer linear programming. Both the active and reactive powers of the grid and resources are incorporated. The model optimizes the following design variables: sitting and sizing of energy storage systems and DGs, depth of discharge, energy of battery, operation pattern of battery, operation pattern of non-renewables units, and investment/operational costs. The proposed model is tested on 69-bus distribution grid. The simulation results show that the depth of discharge is optimized on 30% to 95%. Active and reactive losses achieved by the proposed model are 72% and 47% more accurate compared to the other existing models. The voltage profile is improved by about 8%. The network losses are reduced by 24%. The peak shaving is performed at hours 18 to 24.

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Hybrid cross entropy—cuckoo search algorithm for solving optimal power flow with renewable generators and controllable loads

Sarda

Pandya

Lee

2021

Optim Control Appl Methods

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The demand of energy is increasing due to the growing population of the world and improvements of technology. One of the best significant solution techniques to fulfill this energy demand is utilization of renewable energy sources (RESs). Modern power systems, which integrate RESs, such as wind, small hydro or solar energy sources need to carry out the uncertainty by the accessibility of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow (OPF) problems. This paper proposed a novel hybrid meta‐heuristic algorithm entitled cross entropy—cuckoo search algorithm (CE‐CSA). The application of levy flights in the cuckoo search algorithm (CSA) improves the local exploitation capability while the CE method is used in the initial stage for global exploration due to its fast convergence. The effectiveness of the proposed hybrid algorithm has been demonstrated in solving the OPF problem, considering RESs and controllable loads for different stochastic scenarios in a benchmark system to minimize the total operation cost. To verify its effectiveness, its performance is compared with the most advanced and recently proposed hybrid meta‐heuristic techniques. Simulation results show that the proposed algorithm can solve the OPF problems with RESs and controllable loads efficiently and can give better solutions compared to different techniques. The conventional statistical method called analysis of variance (ANOVA) test, Tukey honestly significant difference test, and Wilcoxon sign rank test are performed for comparative analysis of different techniques. The results of this test show the validation of CE‐CSA compared to different optimization techniques.

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Linear/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations

Cited by 76 publications

References 36 publications

Reduced and aggregated distribution grid representations approximated by polyhedral sets

Reduced and aggregated distribution grid representations approximated by polyhedral sets

Hybrid renewable/nonrenewable/storage resources in electrical grid considering active‐reactive losses and depth of discharge

Hybrid cross entropy—cuckoo search algorithm for solving optimal power flow with renewable generators and controllable loads

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