Computing an optimum direction in control space to avoid stable node bifurcation and voltage collapse in electric power systems

Dobson, Ian; Lu, Liming

doi:10.1109/9.256397

Cited by 157 publications

(81 citation statements)

References 15 publications

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“…We can compute loading margins and their sensitivities using the better known and 263 simpler static load models, while assuming a very general form for the poorly known dynamics which underlie the static equations. This observation generalizes more limited results in [5][6][7] and supports the reductions in [8] of differential-algebraic power system equations to static models. Moreover, this observation is a result underlying advanced industry software to monitor and avoid voltage collapse blackouts, for example [9].…”

Section: Introductionsupporting

confidence: 52%

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

Dobson

2011

NOLTA

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Abstract:The loading margin to a saddle-node or fold bifurcation measures the proximity to voltage collapse blackouts of electric power transmission systems. Sensitivities of the loading margin can be used to select controls to avoid voltage collapse. We analytically justify the use of static models to compute loading margins and their sensitivities and explain how the results apply to underlying dynamic models. The relation between fold bifurcations of the static models and saddle-node bifurcations of the underlying dynamic models is clarified.

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Section: Introductionsupporting

confidence: 52%

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

Dobson

2011

NOLTA

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“…If the contingency is unstable in transient stability terms, a measure is taken to stabilize the power system transient, such as a generator trip. To find effective buses for the reactive power compensation, a sensitivity analysis is then performed at the critical point of the Y-V curve using parametric sensitivity [11], [12]. The formulation for calculating the sensitivity with respect to the reactive power compensation on the ith bus is as follows:…”

Section: A Methods Of Reactive Power Compensation For the Convergence mentioning

confidence: 99%

Determination of Reactive Power Compensation Considering Large Disturbances for Power Flow Solvability in the Korean Power System

Seo

Kang

Lee³

et al. 2011

Journal of Electrical Engineering and Technology

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-This paper proposes a methodology using a tool based on the branch-parameter continuation power flow (BCPF) in order to restore the power flow solvability in unsolvable contingencies. A specified contingency from a set of transmission line contingencies is modeled, considering the transient analysis and practice in the Korean power system. This tool traces a solution path that satisfies the power flow equations with respect to the variation of the branch parameter. At a critical point, in which the branch parameter can move on to a maximum value, a sensitivity analysis with a normal vector is performed to identify the most effective compensation. With the sensitivity information, the location of the reactive power compensation is determined and the effectiveness of the sensitivity information is verified to restore the solvability. In the simulation, the proposed framework is then applied to the Korean power system.

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“…The overall margin sensitivity approach which is generalized in this paper arose in the special case and restricted context of loading margins to voltage collapse caused by fold bifurcation [4], [8]. This paper considers transfer margins to general limits other than voltage collapse.…”

Section: Related Workmentioning

confidence: 99%

“…Write (12) where and are row vectors of Lagrange multipliers. Then, at the optimum solution, it is necessary that , or, equivalently, that (13) (14) (15) Equation (13) is identical to (4), showing that the Lagrange multiplier must be proportional to the vector used in the rest of the paper [the length of the Lagrange multiplier is fixed by (14)]. It is well known in optimization theory (e.g., see [17] or, in the context of applications to minimum cost optimal power flow see [14]) that the sensitivity of the cost function to the constraints is given by the corresponding Lagrange multiplier.…”

Section: B Derivation Of Sensitivity In An Optimization Contextmentioning

confidence: 99%

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Sensitivity of Transfer Capability Margins with a Fast Formula

Greene

Dobson

Alvarado

2002

IEEE Power Eng. Rev.

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Abstract-Bulk power transfers in electric power systems are limited by transmission network security. Transfer capability measures the maximum power transfer permissible under certain assumptions. Once a transfer capability has been computed for one set of assumptions, it is useful to quickly estimate the effect on the transfer capability of modifying those assumptions. This paper presents a computationally efficient formula for the first order sensitivity of the transfer capability with respect to the variation of any parameters. The sensitivity formula is very fast to evaluate. The approach is consistent with the current industrial practice of using dc load flow models and significantly generalizes that practice to more detailed ac power system models that include voltage and reactive power limits. The computation is illustrated and tested on a 3357 bus power system. Index Terms-Optimization, power system control, power system security, power transmission planning, sensitivity.

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Computing an optimum direction in control space to avoid stable node bifurcation and voltage collapse in electric power systems

Cited by 157 publications

References 15 publications

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

The irrelevance of electric power system dynamics for the loading margin to voltage collapse and its sensitivities

Determination of Reactive Power Compensation Considering Large Disturbances for Power Flow Solvability in the Korean Power System

Sensitivity of Transfer Capability Margins with a Fast Formula

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