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Steven H. Low - One of the best experts on this subject based on the ideXlab platform.

  • equivalent relaxations of Optimal Power Flow
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Subhonmesh Bose, Steven H. Low, Thanchanok Teeraratkul, Babak Hassibi
    Abstract:

    Several convex relaxations of the Optimal Power Flow (OPF) problem have recently been developed using both bus injection models and branch Flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch Flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results imply that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.

  • exact convex relaxation of Optimal Power Flow in radial networks
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Lingwen Gan, Ufuk Topcu, Steven H. Low
    Abstract:

    The Optimal Power Flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or Power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial Power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

  • convex relaxation of Optimal Power Flow part ii exactness
    arXiv: Optimization and Control, 2014
    Co-Authors: Steven H. Low
    Abstract:

    This tutorial summarizes recent advances in the convex relaxation of the Optimal Power Flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two Power Flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.

  • convex relaxation of Optimal Power Flow part i formulations and equivalence
    arXiv: Optimization and Control, 2014
    Co-Authors: Steven H. Low
    Abstract:

    This tutorial summarizes recent advances in the convex relaxation of the Optimal Power Flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two Power Flow models, formulates OPF and their relaxations in each model, and proves equivalence relations among them. Part II presents sufficient conditions under which the convex relaxations are exact.

  • Optimal Power Flow in direct current networks
    IEEE Transactions on Power Systems, 2014
    Co-Authors: Lingwen Gan, Steven H. Low
    Abstract:

    The Optimal Power Flow (OPF) problem determines Power generations/demands that minimize a certain objective such as generation cost or Power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and Power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one Optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints.

Kit Po Wong - One of the best experts on this subject based on the ideXlab platform.

  • evolutionary programming based Optimal Power Flow algorithm
    IEEE Transactions on Power Systems, 1999
    Co-Authors: J Yuryevich, Kit Po Wong
    Abstract:

    This paper develops an efficient and reliable evolutionary programming algorithm for solving the Optimal Power Flow (OPF) problem. The class of curves used to describe generator performance does not limit the algorithm and the algorithm is also less sensitive to starting points. To improve the speed of convergence of the algorithm as well as its ability to handle larger systems, the algorithm is enhanced with gradient information. In the paper, the main elements of the evolutionary programming based OPF algorithm are presented. The algorithm is then demonstrated on the IEEE 30 bus test system.

  • evolutionary programming based Optimal Power Flow algorithm
    Power Engineering Society Summer Meeting, 1999
    Co-Authors: J Yuryevich, Kit Po Wong
    Abstract:

    Summary form only given. This paper develops an evolutionary programming (EP) based Optimal Power Flow (OPF) solution algorithm which makes use of an EP load Flow. Solution acceleration concepts are implemented which improve the basic EP algorithm. This acceleration is implemented using the gradient information obtained using the steepest descent method to perform a local search. The method is capable of determining the global optimum solution to the OPF for a range of constraints and objective functions. The algorithm is not sensitive to starting points and is capable of handling nonconvex generator cost curves. The performances of the algorithm when applied to the IEEE 30-bus test system under different generator input-output curves are presented.

Goran Andersson - One of the best experts on this subject based on the ideXlab platform.

  • chance constrained ac Optimal Power Flow reformulations and efficient algorithms
    IEEE Transactions on Power Systems, 2018
    Co-Authors: Line Roald, Goran Andersson
    Abstract:

    Higher levels of renewable electricity generation increase uncertainty in Power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we adopt a chance-constrained AC Optimal Power Flow formulation, which guarantees that generation, Power Flows, and voltages remain within their bounds with a predefined probability. We then discuss different chance-constraint reformulations and solution approaches for the problem. We first describe an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterative solution scheme which alternates between solving a deterministic AC Optimal Power Flow problem and assessing the impact of uncertainty. The flexibility of the iterative scheme enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample-based reformulations that do not require any approximation or relaxation of the AC Power Flow equations. In a case study based on four different IEEE systems, we assess the performance of the method, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical reformulations outperforms the two alternative, sample-based chance constraint reformulations.

  • Optimal Power Flow of multiple energy carriers
    IEEE Transactions on Power Systems, 2007
    Co-Authors: Martin Geidl, Goran Andersson
    Abstract:

    This paper presents an approach for combined optimization of coupled Power Flows of different energy infrastructures such as electricity, gas, and district heating systems. A steady state Power Flow model is presented that includes conversion and transmission of an arbitrary number of energy carriers. The couplings between the different infrastructures are explicitly taken into account based on the new concept of energy hubs. With this model, combined economic dispatch and Optimal Power Flow problems are stated covering transmission and conversion of energy. A general Optimality condition for Optimal dispatch of multiple energy carriers is derived, and the approach is compared with the standard method used for electrical Power systems. Finally, the developed tools are demonstrated in examples

  • Use of UPFC for Optimal Power Flow control
    IEEE Transactions on Power Delivery, 1997
    Co-Authors: M. Noroozian, L. Angquist, Mehrdad Ghandhari, Goran Andersson
    Abstract:

    This paper deals with Optimal Power Flow control in electric Power systems by the use of a unified Power Flow controller (UPFC). Models suitable for incorporation in Power Flow programs are developed and analysed. The application of UPFC for Optimal Power Flow control is demonstrated through numerical examples. It is shown that a UPFC has the capability of regulating the Power Flow and minimising the Power losses simultaneously. An algorithm is proposed for determining the optimum size of UPFC for Power Flow applications. The performance of UPFC is compared with that of a phase shifting transformer (PST).

J Yuryevich - One of the best experts on this subject based on the ideXlab platform.

  • evolutionary programming based Optimal Power Flow algorithm
    IEEE Transactions on Power Systems, 1999
    Co-Authors: J Yuryevich, Kit Po Wong
    Abstract:

    This paper develops an efficient and reliable evolutionary programming algorithm for solving the Optimal Power Flow (OPF) problem. The class of curves used to describe generator performance does not limit the algorithm and the algorithm is also less sensitive to starting points. To improve the speed of convergence of the algorithm as well as its ability to handle larger systems, the algorithm is enhanced with gradient information. In the paper, the main elements of the evolutionary programming based OPF algorithm are presented. The algorithm is then demonstrated on the IEEE 30 bus test system.

  • evolutionary programming based Optimal Power Flow algorithm
    Power Engineering Society Summer Meeting, 1999
    Co-Authors: J Yuryevich, Kit Po Wong
    Abstract:

    Summary form only given. This paper develops an evolutionary programming (EP) based Optimal Power Flow (OPF) solution algorithm which makes use of an EP load Flow. Solution acceleration concepts are implemented which improve the basic EP algorithm. This acceleration is implemented using the gradient information obtained using the steepest descent method to perform a local search. The method is capable of determining the global optimum solution to the OPF for a range of constraints and objective functions. The algorithm is not sensitive to starting points and is capable of handling nonconvex generator cost curves. The performances of the algorithm when applied to the IEEE 30-bus test system under different generator input-output curves are presented.

P.r. Bijwe - One of the best experts on this subject based on the ideXlab platform.

  • Day-Ahead and Real Time Optimal Power Flow considering Renewable Energy Resources
    International Journal of Electrical Power and Energy Systems, 2016
    Co-Authors: S. Surender Reddy, P.r. Bijwe
    Abstract:

    In practice, the Real Time Optimal Power Flow (RT-OPF) is performed in every 5-15 min intervals, and the Day-Ahead Optimal Power Flow (DA-OPF) is performed in every 1 h intervals with the static snapshot forecast data. During the period between two consecutive schedules, the generators participate in managing Power imbalance, based on participation factors from previous Economic Dispatch (ED)/Optimal Power Flow (OPF). In modern Power system with considerable Renewable Energy Resources (RERs) that have high variability, this conventional approach may not adequately accommodate the economic implication of the said variability. This paper proposes the evaluation of 'best-fit' participation factors by taking into account the minute-to-minute variability of solar, wind and load demand for RT-OPF, and every 15 min variability for DA-OPF, over a scheduling period. The voltage, reactive Power limit and line Flow constraints are included for all minute-to-minute sub-intervals for RT-OPF and for every 15 min sub-intervals for DA-OPF. From the system security point of view, voltage stability index is calculated in DA-OPF and RT-OPF approaches. Since 'best-fit' participation factors are evaluated only once, i.e., at the start of scheduling interval, the dimensionality of optimization problem remains the same as that of conventional approach. IEEE 30 bus system is used to test the effectiveness of the proposed approach in terms of system security and economical benefit.