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About 10,000 papers for “Optimal Power Flow Distribution”
Jordan Radosavljević · Institution of Engineering and Technology eBooks · 2018
In this chapter, a generalized approach for the OPF analysis in distribution networks is presented. This implies the inclusion of different types of DG units, taking into account the uncertainties of the input variables, the multiobjective optimization, and application of efficient metaheuristic methods for solving the OPF problem.
Cited by 15
Institution of Engineering and Technology eBooks · 2024
Cited by 13
Bala Venkatesh · 2010 Conference Proceedings IPEC · 2010
Radial distribution systems (RDS) have lines with high R/X ratios and hence Newton based methods were not reliable to solve their set of bus power balance equations. Historically, a recursive solution method using a set of voltage equations and its variants are very popular to determine a voltage solution of a RDS. Consequently, use of classical optimization was not possible. Recent developments in the last decade have created a system of equations that can be reliably solved using first order Newton Raphson method to determine a voltage solution of a RDS. This opens up the possibility of using classical optimization method for optimizing these systems. This paper uses this new load flow method to determine optimal setting of controllers in a RDS such that its real power losses are minimized and voltage magnitudes are acceptable. This method is completely described along with its theory. It is tested on popular RDS examples found in literature.
Cited by 7
Kyri Baker, Emiliano Dall’Anese, Tyler Summers · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2016
Cited by 1
Ashraf Ramadan, Mohamed Ebeed, Salah Kamel et al. · Elsevier eBooks · 2020
Cited by 18
Institution of Engineering and Technology eBooks · 2024
Cited by 0
Simon Sepulveda, Alejandro Garcés, Juan José Mora Flórez · Greater South Information System · 2023
Abstract Active distribution networks (ADN) may operate in different modes according to the generation demand balance and the capacity of the primary grid for imposing a constant frequency. Conventionally, a customized optimization model is used for each operating mode. Unlike that conventional approach, this article proposes a general optimization model capable of operating the system in three different modes: grid-connected, islanded with a surplus of generation, and islanded with a deficit of generation. Real-time operation is required in this framework with guarantees such as global optimum, uniqueness of the solution, and fast algorithm convergence; for this reason, a convex approach is employed for grid modeling. Numerical experiments demonstrate that the proposed optimization-based operation model can handle the three types of operation while ensuring the safety operation with frequency and voltage within expected limits.
Cited by 0Open access
Vladimir Dvorkin, Ferdinando Fioretto, Pascal Van Hentenryck et al. · IEEE Transactions on Power Systems · 2020
Although distribution grid customers are obliged to share their consumption data with distribution system operators (DSOs), a possible leakage of this data is often disregarded in operational routines of DSOs. This paper introduces a privacy-preserving optimal power flow (OPF) mechanism for distribution grids that secures customer privacy from unauthorised access to OPF solutions, e.g., current and voltage measurements. The mechanism is based on the framework of differential privacy that allows to control the participation risks of individuals in a dataset by applying a carefully calibrated noise to the output of a computation. Unlike existing private mechanisms, this mechanism does not apply the noise to the optimization parameters or its result. Instead, it optimizes OPF variables as affine functions of the random noise, which weakens the correlation between the grid loads and OPF variables. To ensure feasibility of the randomized OPF solution, the mechanism makes use of chance constraints enforced on the grid limits. The mechanism is further extended to control the optimality loss induced by the random noise, as well as the variance of OPF variables. The paper shows that the differentially private OPF solution does not leak customer loads up to specified parameters.
Cited by 5Open access
Simón Sepúlveda-García, Alejandro Garcés, Juan José Mora Flórez · Electrical Engineering · 2023
Abstract Active distribution networks (ADN) may operate in different modes according to the generation demand balance and the capacity of the primary grid for imposing a constant frequency. Conventionally, a customized optimization model is used for each operating mode. Unlike that conventional approach, this article proposes a general optimization model capable of operating the system in three different modes: grid-connected, islanded with a surplus of generation, and islanded with a deficit of generation. Real-time operation is required in this framework with guarantees such as global optimum, uniqueness of the solution, and fast algorithm convergence; for this reason, a convex approach is employed for grid modeling. Numerical experiments demonstrate that the proposed optimization-based operation model can handle the three types of operation while ensuring the safety operation with frequency and voltage within expected limits.
Cited by 4Open access
Leisi Dai, Huangqing Xiao, Ping Yang · Frontiers in Energy Research · 2024
This paper proposes an optimal power flow model that takes into account the uncertainty in the probability distribution of wind power. The model can schedule controllable generators under any possible distribution of wind power to ensure the safe and economic operation of the system. Firstly, considering the incompleteness of historical wind power data, the paper models the uncertainty of wind power using second-order moments of probability distribution and their fluctuation intervals. Subsequently, a robust optimal power flow model based on probability distribution model and joint chance constraints is established. The Lagrangian duality theorem is then employed to eliminate random variables from the optimization model, transforming the uncertainty model into a deterministic linear matrix inequality problem. Finally, a convex optimization algorithm is used to solve the deterministic problem, and the results are compared with traditional chance-constrained optimal power flow model. The feasibility and effectiveness of the proposed method are validated through case study simulations.
Cited by 3Open access
Zhongjie Guo, Wei Wei, Laijun Chen et al. · IEEE Transactions on Power Systems · 2021
The output of renewable generation depends on the real-time weather conditions and changes rapidly; so the economic operating point of the power system varies over time. This paper aims to find the explicit mapping from variable renewable power to optimal power flow solutions. To this end, we propose a parametric distribution optimal power flow (P-DOPF) method, which gives the optimal dispatch strategy and power flow status as analytical functions of the renewable output. With the established distribution optimal power flow problem based on the relaxed Distflow model, the first step is to perform a global polyhedral approximation on the second-order cone constraints to develop a linearized formulation. The second step is to obtain the P-DOPF model by treating renewable power output as parameters; then, the P-DOPF problem gives rise to a multi-parametric linear program (mp-LP). Third, we prove that the optimal solution and optimal value of the P-DOPF are piecewise linear functions of the parameters and we design an adaptive-sampling algorithm to construct the optimal value and optimal solution functions, as well as the partition of the parameter set, subject to a given error tolerance; this algorithm is not influenced by model degeneracy, a common difficulty of existing mp-LP algorithms. The P-DOPF framework provides an explicit real-time control policy of generators in response to the renewable output. Case studies on the IEEE 33 and 69-bus systems verify the effectiveness and performance of the proposed method; by comparison, the proposed method outperforms the established affine policy method in computational efficiency and optimality by 24.5% and 4.62%, respectively.
Cited by 25
Xiaoning Kang, Xiuda Ma, Hao Wang et al. · 2016
The goal of maintaining system operation stability, improving reliability and reducing loss in DC distribution system can be achieved through optimal power flow (OPF). Firstly, a multi-objective OPF model of DC distribution system targeting on reducing system total fault rate and power loss is established with consideration of constrains including converter capacity, operation safety and the charge-discharge rate of energy storage devices. The multi-objective optimization of power flow is converted into single objective optimization using the lexicographically stratified method, then it's solved effectively by second-order cone programming. Finally, through multi-period simulation of a 5 node system, the efficiency and accuracy features of the proposed method is verified, and the algorithm achieves optimization of both reliability and economic efficiency.
Cited by 1
Sarmad Hanif, Rabayet Sadnan, Tylor Slay et al. · 2023
Due to changes in electric distribution grid operation, new operation regimes have been recommended. Distribution grid optimal power flow (DOPF) has received tremendous attention in the research community, yet it has not been fully adopted across the utility industry. Our paper recognizes this problem and suggests a development and integration procedure for DOPF. We propose development of DOPF as a three step procedure of 1) processing the grid, 2) obtaining a tractable solution, and 3) implementing multiple solution algorithms and benchmarking them to improve application reliability. For the integration of DOPF, we demonstrate how a DOPF federate may be developed that can be integrated in a co-simulation environment to mimic the real-world conditions and hence improve its practicality to be deployed in the field. To demonstrate the efficacy of the proposed methods, tests on IEEE 123-bus system are performed where the usage of tractable formulation in DOPF algorithm development and its comparison to the benchmark solution are demonstrated.
Cited by 1
Ellingsen, Matias Lunde · Duo Research Archive (University of Oslo) · 2020
Når kraftnettet nå moderniseres, trengs det smarte løsninger for effektiv og sikker planlegging og drift av systemene. Tradisjonelle optimeringsteknikker får fornyet oppmerksomhet siden de nå blir relevante i nye anvendelser. «Security Constrained Optimal Power Flow» (SCOPF) er en utvidelse av optimal lastflyt (OPF). Hensikten med SCOPF er vanligvis å finne den mest kostnadseffektive fordelingen av kraftproduksjon i et system, samtidig som alle begrensninger overholdes, både nå og under en rekke eventualiteter, som utfall av enkelte linjer eller generatorer. Brorparten av eksisterende SCOPF programvare lener seg enten på DC tilnærminger, som ikke egner seg for distribusjonsnett, er ikke åpent tilgjengelig, eller tar ikke hensyn til muligheten for korrigerende handlinger ved inntrufne eventualiteter. \n\nMed utgangspunkt i et utvalg tilgjengelig litteratur, et grunnlag for forståelse og løsning av SCOPF problemet presenteres, og en spesifikk løsningsstrategi identifiseres og legges fram. Optimal lastflyt-problemet løses ved sekvensiell lineær programmering, inkludert en tillitsregion-metode. Med denne tilnærmingen lineariseres problemet rundt en nåværende løsning og løses iterativt med lineær programmering. Tillitsregion-metoden justerer området hvor lineariseringen er antatt å være gyldig med utgangspunkt i nøyaktigheten av forrige iterasjons løsning. For å løse SCOPF-problemet, hvor begrensninger som følge av eventualiteter også må tas med, brukes Bender’s dekomposisjon. Det involverer å dekomponere problemet til et masterproblem og en rekke underproblemer for hver eventualitet. Disse løses også iterativt, og fra underproblemer hvor det oppdages overskridelser genereres det lineære begrensinger som legges til masterproblemet. Den presenterte algoritmen er designet til å kunne vurdere både forebyggende sikkerhet og korrigerende sikkerhet. \n\nProgrammet testes og demonstreres på to illustrerende systemer med noen numeriske eksempler. Den foreslåtte optimal lastflyt-algoritmen presterer bra på eksempelsystemet med 6 samleskinner. Her kreves 9 iterasjoner, og løsningen gir en kostnadsreduksjon på 5,45 % sammenlignet med utgangspunktet. SCOPF-algoritmen demonstreres på et eksempelsystem med 12 samleskinner. «Forebyggende sikkerhet» og «korrigerende sikkerhet» resulterer i en kostnadsøkning på henholdsvis 1,25 % og 0.41 % sammenlignet med standard optimal lastflytløsning. Tester av de vurderte eventualitetene viser at løsningene holder, men at løsningen ved «korrigerende sikkerhet» kan være unøyaktig hvis større korrigerende handlinger tillates. Det konkluderes med at de brukte metodene virker lovende, og med videre arbeid kan bli nyttige verktøy i planlegging og drift av fremtidens distribusjonsnett.
Cited by 0Open access
Biao Li, Can Wan, Yunyi Li et al. · IET Generation Transmission & Distribution · 2023
Abstract Optimal power flow (OPF) plays an important role in the secure and economical operation of the distribution network. This paper proposes a novel generalized linear‐constrained optimal power flow (GLOPF) model for both radial and mesh distribution networks, which iteratively approaches the optimal solution to the original OPF problem. The first‐order Taylor series approximation method is applied to linearize the non‐linear and non‐convex power flow constraints for a given Taylor expansion point (TEP). In addition, the objective function of the GLOPF model is only added with an easy‐compute second‐order penalty on state variables, which is at least positive semi‐definite and guarantees the convexity of the quadratic optimization. Then a TEP‐based iterative (TEP‐I) method is proposed in the GLOPF model to construct a series of linear‐constrained convex quadratic optimizations, which avoids the complex calculation of quasi‐Hessian or Hessian matrices in traditional sequential programming methods. The converged solution to the GLOPF model is proved to satisfy the Karush–Kuhn–Tucker conditions of the original OPF problem. Furthermore, the GLOPF model at first and second iterations can be implemented as the ‘cold‐start’ and ‘warm‐start’ LOPF models, respectively. Case studies verify the super‐linear convergence and high accuracy of the proposed GLOPF model.
Cited by 15Open access
Lusha Wang, Ravi Raj Shrestha, Anamika Dubey · IEEE Transactions on Smart Grid · 2025
Recent advancements in urban electrification have reshaped power distribution, yet most optimization research remains limited to radial feeders and simplified models that overlook the role of transformers and secondary networks—where most distributed energy resources (DERs) are connected. In practice, urban grids often feature heavily meshed secondary networks, creating challenges for accurate and tractable power flow optimization. Existing formulations for meshed networks are typically based on bus injection models and balanced assumptions, which hinder effective linearization and scalability. This paper presents a linearized branch flow model for unbalanced, multi-phase distribution systems with arbitrary topologies and detailed transformer representations. A unified linear meshed power flow (LM-PF) and optimal power flow (LM-OPF) formulation is derived for radial, weakly meshed, and heavily meshed networks, supported by new linearized angle recovery conditions. The proposed model explicitly addresses the trade-off between accuracy and tractability by providing theoretical error bounds and comparisons with existing nonlinear optimization (NL-OPF) methods. Extensive case studies were conducted on the radial and meshed IEEE 13-node feeder, the meshed IEEE 123-node feeder, and the heavily meshed IEEE 342-node feeder. These include: (i) power-flow validation under varying loading conditions, (ii) optimization-based comparison with the nonlinear OPF for cycle-constraint validation, and (iii) power-flow accuracy evaluation on networks with a large number of transformers under diverse loading scenarios. These results confirm that the proposed LM-PF, LM-OPF, and transformer modeling framework is highly accurate, scalable, and enables optimization-friendly formulations suitable for large-scale distribution system applications.
Cited by 0
Ridley Osei Assib Annin · Purdue · 2026
Distributed energy resources (DERs) can be scheduled in a coordinated way by the distribution system operator (DSO) to delay or prevent costly capacity upgrades. However, the lack of comprehensive data at the distribution grid level renders real-time scheduling of DERs with the optimal power flow (OPF) ineffective. Consequently, DSOs may need to coordinate DERs using limited data until smart meters are widely implemented. How much data is necessary for optimal DER scheduling? Does the DSO need to know the load demands at each feeder bus to solve an OPF?This thesis leverages redundancies in the structure and data of OPFs to reduce communication requirements while examining the tradeoff between data compression and grid performance. An OPF data distillation framework comprising two steps is proposed: first, the DSO collects OPF data in near-real time from only a subset of nodes; second, it reconstructs the full OPF data from this limited information and feeds it into the OPF solver. The selection and reconstruction of OPF data can be performed to maximize the fidelity of the reconstructed data or the resulting OPF solutions. In the first approach, OPF data distillation is formulated as a sparsity-regularized convex problem. In the second approach, it is presented as a sparsity-regularized bilevel program, both of which are solved using proximal gradient algorithms. The latter approach offers a better approximation of OPF solutions but with increased complexity. Numerical tests demonstrate that the second approach improves the fidelity and feasibility of the reconstructed OPF solutions, which can be approximated reasonably well even from partial data.
Cited by 0Open access
C. Mylonas, Stavros Karagiannopoulos, Petros Aristidou et al. · IET conference proceedings. · 2021
Cited by 5
Dinesh Kumar Mahto, Vikash Kumar Saini, Akhilesh Mathur et al. · 2021 5th International Conference on Information Systems and Computer Networks (ISCON) · 2021
Optimal power flow (OPF) provides solutions to power flow problem like network loss minimization and voltage profile improvement in the distribution network. This task is achieved by the optimal setting of control variables subjected to operational constraint. Traditionally, OPF solutions are calculated by model-driven approaches which are based on mathematical assumption. The accuracy of these model based depends on the theoretical concept like convexity, differentiability and continuity. Accuracy of the model is subjected to system constraint which makes it less robust to implement. In recent time, massive deployment of sensor based measuring devices into the network which acquires large amount of data for analysis. It facilitates data driven approaches over model-based approaches. This paper studies Data- driven ANN model for mapping of input parameters (PD, QD) and output parameters(V,) to emulate actual system. Additionally, three weight training algorithms namely (a) Levenberg-Marquardt (LM), (b) Bayesian Regularization (BR), and (c) Scaled Conjugate Gradient (SCG)are compared with MATPOWER embedded solver (MIPS) on the standard IEEE-33 bus distribution network. The LM, BR, and SCG based ANN models have the computational time of 0.009511,0.009129, and 0.011519 seconds respectively. It shows that the proposed BR- based models outperform rest of models, and also it is 254 time faster than the traditional MIPS solver.
Cited by 9
Hao Jiao, Jinming Chen, Xindong Zhao et al. · 2022
With the access of distributed new energy sources and loads, the coupling relationship between the transmission and the distribution network is greatly enhanced. In order to adapt to the increasing coupling relationship between transmission and distribution, this paper proposes a generalized global optimization model for transmission and distribution. Considering the carbon reduction requirements of the power industry in the context of carbon peak and carbon neutral, the coordinated transmission and distribution optimal power flow (TDOPF) model with carbon emission constraints is proposed. Based on the different characteristics of the transmission and distribution network, the heterogeneous decomposition algorithm is used to solve the optimization model. The transmission and distribution network is alternately optimized. The auxiliary function is constructed by parameters such as boundary node voltage and injection power to ensure that the optimal conditions of the global network are satisfied. The numerical example test shows the proposed algorithm has great accuracy and convergence.
Cited by 0