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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 computational framework for risk-based power system operations under uncertainty: Part II: Case studies2015In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 119, p. 66-75Article in journal (Refereed)
    Abstract [en]

    With larger penetrations of wind power, the uncertainty increases in power systems operations. The wind power forecast errors must be accounted for by adapting existing operating tools or designing new ones. A switch from the deterministic framework used today to a probabilistic one has been advocated. This two-part paper presents a framework for risk-basedoperations of power systems. This framework builds on the operating risk defined as the probability of the system to be outside the stable operation domain, given probabilistic forecasts for the uncertainty, load and wind power generation levels. This operating risk can be seen as a probabilistic formulation of the N - 1 criterion. In Part I, the definition of the operating risk and a method to estimate it were presented. A new way of modeling the uncertain wind power injections was presented. In Part II of the paper, the method's accuracy and computational requirements are assessed for both models. It is shown that the new model for wind power introduced in Part I significantly decreases the computation time of the method, which allows for the use of later and more accurate forecasts. The method developed in this paper is able to tackle the two challenges associated with risk-based real-time operations: accurately estimating very low operating risks and doing so in a very limited amount of time.

  • 2.
    Hamon, Camille
    et al.
    KTH Royal Institute of Technology.
    Perninge, Magnus
    KTH Royal Institute of Technology.
    Söder, Lennart
    KTH Royal Institute of Technology.
    A computational framework for risk-based power systems operations under uncertainty: Part I: Theory2015In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 119, p. 45-53Article in journal (Refereed)
    Abstract [en]

    With larger penetrations of wind power, the uncertainty increases in power systems operations. The wind power forecast errors must be accounted for by adapting existing operating tools or designing new ones. A switch from the deterministic framework used today to a probabilistic one has been advocated. This two-part paper presents a framework for risk-basedoperations of power systems. This framework builds on the operating risk defined as the probability of the system to be outside the stable operation domain, given probabilistic forecasts for the uncertainty (load and wind power generation levels) and outage rates of chosen elements of the system (generators and transmission lines). This operating risk can be seen as a probabilistic formulation of the N - 1 criterion. The stable operation domain is defined by voltage-stability limits, small-signal stability limits, thermal stability limits and other operating limits. In Part I of the paper, a previous method for estimating the operating risk is extended by using a new model for the joint distribution of the uncertainty. This new model allows for a decrease in computation time of the method, which allows for the use of later and more up-to-date forecasts. In Part II, the accuracy and the computation requirements of the method using this new model will be analyzed and compared to the previously used model for the uncertainty. The method developed in this paper is able to tackle the two challenges associated with risk-based real-time operations: accurately estimating very low operating risks and doing so in a very limited amount of time.

  • 3.
    Hamon, Camille
    et al.
    Norwegian University of Science and Technology, Norway.
    Perninge, Magnus
    Lund University.
    Söder, Lennart
    KTH Royal Institute of Technology.
    An importance sampling technique for probabilistic security assessment in power systems with large amounts of wind power2016In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 131, p. 11-18Article in journal (Refereed)
    Abstract [en]

    Larger amounts of variable renewable energy sources bring about larger amounts of uncertainty in the form of forecast errors. When taking operational and planning decisions under uncertainty, a trade-off between risk and costs must be made. Today's deterministic operational tools, such as N-1-based methods, cannot directly account for the underlying risk due to uncertainties. Instead, several definitions of operating risks, which are probabilistic indicators, have been proposed in the literature. Estimating these risks require estimating very low probabilities of violations of operating constraints. Crude Monte-Carlo simulations are very computationally demanding for estimating very low probabilities. In this paper, an importance sampling technique from mathematical finance is adapted to estimate very low operating risks in power systems given probabilistic forecasts for the wind power and the load. Case studies in the IEEE 39 and 118 bus systems show a decrease in computational demand of two to three orders of magnitude.

  • 4.
    Perninge, Magnus
    KTH Royal Institute of Technology.
    Approximating the loadability surface in the presence of SNB–SLL corner points2013In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 96, p. 64-74Article in journal (Refereed)
    Abstract [en]

    Power system voltage security assessment is generally applied by considering the power system loadability surface. For a large power system, the loadability surface is a complicated hyper-surface in parameter space, and local approximations are a necessity for any analysis. Unfortunately, inequality constraints due to for example generator overexitation limiters, and higher codimension bifurcations, make the loadability surface non-smooth. One situation that is particularly difficult to handle is when a saddle-node bifurcation surface intersects a switching loadability limit surface. In this article we intend to investigate how several local approximations can be combined to obtain an adequate approximation of the loadability surface near such intersections.

  • 5.
    Perninge, Magnus
    Lund University.
    Approximating the parameter-space stability boundary considering post-contingency corrective controls2015In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 121, p. 313-324Article in journal (Refereed)
    Abstract [en]

    Lately, much work in the area of voltage stability assessment has been focused on finding post-contingency corrective controls. In this article a contribution to this area will be presented where we investigate the surface of maximal loadability while allowing for post-contingency corrective controls. This objective is different from the usual, where the aim is to include the post-contingency controls in a security-constrained optimal power flow. Our aim is rather to find approximations of the post-contingency stability boundary, in pre-contingencyparameter space, while including the possibility for post-contingency corrective controls. These approximations can then be used in, for example, a chance-constrained optimal power flow routine.

  • 6.
    Perninge, Magnus
    Lund University.
    Stochastic optimal power flow by multi-variate Edgeworth expansions2014In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 109, p. 90-100Article 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 steady-state variable limits have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. Recently an extension of the stochastic optimal power flow formulation that included constraints for voltage stability as well as small-signal stability was proposed. This was done by approximating the voltage stability and small-signal stability constraint boundaries with second order approximations in parameter space. In this article an alternative solution method to this problem will be proposed. The new improved solution method, which is based on Edgeworth series expansions, is both more efficient and accurate. We also give details on convexity of the problem and discuss some computational issues.

  • 7.
    Perninge, Magnus
    et al.
    Royal Institute of Technology.
    Söder, Lennart
    Royal Institute of Technology.
    Optimal activation of regulating bids to handle bottlenecks in power system operation2012In: Electric power systems research, ISSN 0378-7796, E-ISSN 1873-2046, Vol. 83, no 1, p. 151-159Article in journal (Refereed)
    Abstract [en]

    In this article we investigate how to optimally activate regulating bids to handle bottlenecks in power system operation. This will lead to an optimal stopping problem, and activation of a regulating bid is to be performed when the transfer through a specific system bottleneck reaches a certain value. Compared to previous research in the area the work presented in this article includes a more detailed model of the structure of the regulating market, and reaction times of actors on the regulating market is taken into consideration. The emphasis of the presentation will be application to a two area test system. The method is compared to Monte Carlo simulation in a numerical example. The example shows a promising result for the suggested method.

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