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  • 1.
    Hamon, Camille
    et al.
    KTH Royal Institute of Technology.
    Perninge, Magnus
    KTH Royal Institute of Technology.
    Söder, Lennart
    KTH Royal Institute of Technology.
    A stochastic optimal power flow problem with stability constraints: Part I: Approximating the stability boundary2013In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 2, p. 1839-1849Article in journal (Refereed)
    Abstract [en]

    Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only line flows have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint boundaries with second-order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this first part of the paper, we derive second-order approximations of stability boundaries in parameter space. In the second part, the approximations will be used to solve a stochastic optimal power flow problem.

  • 2.
    Perninge, Magnus
    et al.
    KTH Royal Institute of Technology.
    Hamon, Camille
    KTH Royal Institute of Technology.
    A stochastic optimal power flow problem with stability constraints: Part II: the optimization problem2013In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 28, no 2, p. 1849-1857Article in journal (Refereed)
    Abstract [en]

    Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on line flows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint surfaces with second-order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this, the second part of the paper, we look at how Cornish-Fisher expansion combined with a method of excluding sets that are counted twice, can be used to estimate the probability of violating the stability constraints. We then show in a numerical example how this leads to an efficient solution method for the stochastic optimal power flow problem.

  • 3.
    Perninge, Magnus
    et al.
    Royal Institute of Technology.
    Lindskog, Filip
    Royal Institute of Technology.
    Söder, Lennart
    Royal Institute of Technology.
    Importance sampling of injected powers for electric power system security analysis2012In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 27, no 1, p. 3-11Article in journal (Refereed)
    Abstract [en]

    Power system security analysis is often strongly tied with contingency analysis. To improve Monte Carlo simulation, many different contingency selection techniques have been proposed in the literature. However, with the introduction of more variable generation sources such as wind power and due to fast changing loads, power system security analysis will also have to incorporate sudden changes in injected powers that are not due to generation outages. In this paper, we use importance sampling for injected-power simulation to estimate the probability of system failure given a power system grid state. A comparison to standard crude Monte Carlo simulation is also performed in a numerical example and indicates a major increase in simulation efficiency when using the importance sampling technique proposed in the paper.

  • 4.
    Perninge, Magnus
    et al.
    KTH Royal Institute of Technology.
    Söder, Lennart
    KTH Royal Institute of Technology.
    A stochastic control approach to manage operational risk in power systems2012In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 27, no 2, p. 1021-1031Article in journal (Refereed)
    Abstract [en]

    In this paper, the novel method operational risk managing optimal power flow (ORMOPF), for minimizing the expected cost of power system operation, is proposed. In contrast to previous research in the area, the proposed method does not use a security criterion. Instead the expected cost of operation includes expected costs of system failures.

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