Appearance of multiple stable load flow solutions under power flow reversal conditions

Nguyen, Hung D.; Turitsyn, Konstantin

doi:10.1109/pesgm.2014.6938797

Cited by 39 publications

(25 citation statements)

References 24 publications

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“…Let v, s := (( s Y ) T , ( s ∆ ) T ) T be a given solution to the fixed point equation (4). For a given power injection vector s := ((s Y ) T , (s ∆ ) T ) T , consider the first iteration of the fixed-point method (6)…”

Section: B Fixed-point Linearization (Fpl) Methodsmentioning

confidence: 99%

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

Bernstein

Wang

Dall’Anese

et al. 2018

IEEE Trans. Power Syst.

152

127

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This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders. 1 We note that models (iii) and (iv) are the same in terms of the mathematical formulation. However, from the practical point of view, model (iv) reflects an actual mode of connection on the secondary side of the distribution transformer, whereas model (iii) pertains to the case where different distribution transformers are lumped in the same bus for network reduction purposes.

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Section: B Fixed-point Linearization (Fpl) Methodsmentioning

confidence: 99%

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

Bernstein

Wang

Dall’Anese

et al. 2018

IEEE Trans. Power Syst.

152

127

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“…DGs, are integrated to the systems, especially on the distribution level. When the penetration level becomes very high the traditional static voltage stability may be insufficient to assess the system security [37], [45]. On the other hand, the approach proposed in this work is valid, at least for non-synchronous DGs that can be modelled as a negative loads with dynamics in the form of (2) and (3).…”

Section: B Robust Stabilitymentioning

confidence: 96%

Robust Stability Assessment in the Presence of Load Dynamics Uncertainty

Nguyen

Turitsyn

2016

IEEE Trans. Power Syst.

Self Cite

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Abstract-Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical "robust stability" criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of Robust Stability Assessment (RSA) that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies.

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“…Since V k (α) and W k (α) are holomorphic [33], we can use power series to represent them. Then, (9) can be re-written as…”

Section: A Holomorphic Embedding Of Power Flow Equations 1) Pq Bus Ementioning

confidence: 99%

Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

Wang

2019

IEEE Access

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In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Padé approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.

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Appearance of multiple stable load flow solutions under power flow reversal conditions

Cited by 39 publications

References 24 publications

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

Robust Stability Assessment in the Presence of Load Dynamics Uncertainty

Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

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