A Hybrid Approach for Efficient Robust Design of Dynamic Systems

̈nnigmann, Martin Mo; Marquardt, Wolfgang; Bischof, Christian; Beelitz, Thomas; Lang, Bruno; Willems, Paul R.

doi:10.1137/s003614450444662x

Cited by 25 publications

(19 citation statements)

References 9 publications

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“…We note that further investigations considering voltage dynamics may be of interest, but are not considered here. Lower and upper bounds (4) are imposed on the bus voltages to ensure feasible grid operation. Similarly, generator active and reactive powers are bounded according to (5a) (5b)…”

Section: B Electromechanical Dynamicsmentioning

confidence: 99%

“…Power plants running at maximum load, however, are likely not to be able to provide sufficient reserves to cope with variability of consumption. Moreover, aggressive cost optimization may drive dynamical systems to stability boundaries [2]- [4]. An increasing amount of energy from uncertain sources, such as wind or solar energy, results in additional reliability issues that call for a simultaneous consideration of cost optimality and robust stability.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to the authors mentioned above we do not need to augment the economic optimization by an additional computational loop that computes or maximizes stability margins, or calculates or approximates critical eigenvalues. Essentially, we track the distance to stability boundaries implicitly by stating additional nonlinear constraints in the cost optimization problem [2]- [4]. These so called normal vector constraints render a simultaneous or a priori calculation of stability boundaries obsolete.…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed stability in optimal power generation dispatching under uncertainty

Grote

Kastsian

Mönnigmann

2013

IEEE Trans. Power Syst.

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Stability and cost optimality of power generation and supply systems must not be considered independently from one another. Simple examples show that optimizing cost without considering stability may result in modes of operation that, while economically optimal, are unstable. We demonstrate that stability, robustness, and optimality can be considered systematically and simultaneously by combining bifurcation theory and nonlinear optimization. Essentially, the proposed method enforces a backoff distance between the optimal point of operation and operational or stability boundaries in the space of the optimization variables, where bifurcation theory is used to describe nonlinear stability boundaries.We optimize a simple grid to demonstrate the features of the proposed approach. Our results show that the method can be applied to problems with both continuous and Boolean optimization variables, where the latter represent grid breakers in the example. The constraints for robust stability turn out to be crucial in that economically optimal but unstable modes of operation exist despite the small size of the illustrative example. Our results demonstrate that the robustness constraints can affect the optimal value of the Boolean variables. We show that the method provides a measure for the cost of stability and robustness.

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Section: B Electromechanical Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Guaranteed stability in optimal power generation dispatching under uncertainty

Grote

Kastsian

Mönnigmann

2013

IEEE Trans. Power Syst.

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“…This basic framework entails a whole family of so-called normal vector methods [2], [3] which enforce constraints on the distance between the critical manifold and the robustness region in parameter space [4], [5] as a criterion for robustness. Critical manifolds here represent those boundaries in parameter space where a feasibility or stability constraint violation occurs.…”

Section: = G(x Y P δ(D T))mentioning

confidence: 99%

Stability-Preserving Optimization in the Presence of Fast Disturbances

Wirth

Gerhard

Marquardt

2011

IEEE Trans. Automat. Contr.

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We present a method to robustly optimize a set of design parameters for a dynamical system which is subject to fast disturbances. These disturbances are themselves parameterized by a finite number of parameters. Robustness is ensured by requiring the disturbance parameters to stay sufficiently far away from critical manifolds in the parameter space, at which the system would lose stability. These manifolds are defined by an algebraic condition on the system trajectories. The closest distance to the critical manifolds is measured along their normal vectors.

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“…For efficiency reasons, however, standard floating-point techniques should be employed whenever possible. Therefore we have developed a two-stage approach for process design [18]. In the first stage a conventional constrained optimizer is used to locate an optimal point of operation, the constraints being chosen in such a way that with high probability there is no singularity in its vicinity.…”

Section: Introductionmentioning

confidence: 99%

Efficient Task Scheduling in the Parallel Result-Verifying Solution of Nonlinear Systems

2006

Self Cite

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Nonlinear systems occur in diverse applications, e.g., in the steady state analysis of chemical processes. If safety concerns require the results to be provably correct then result-verifying algorithms relying on interval arithmetic should be used for solving these systems. Since such algorithms are very computationally intensive, the coarse-grained inter-box parallelism should be exploited to make them feasible in practice. In this paper we briefly describe our framework SONIC for the verified solution of nonlinear systems and give detailed information about its parallelization with OpenMP and MPI. Our numerical results show that the implemented parallelization schemes are indeed successful. The more sophisticated MPI implementation seems to be superior to the easy-to-implement OpenMP version and shows almost linear speedup up to a large number of processors.

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A Hybrid Approach for Efficient Robust Design of Dynamic Systems

Cited by 25 publications

References 9 publications

Guaranteed stability in optimal power generation dispatching under uncertainty

Guaranteed stability in optimal power generation dispatching under uncertainty

Stability-Preserving Optimization in the Presence of Fast Disturbances

Efficient Task Scheduling in the Parallel Result-Verifying Solution of Nonlinear Systems

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