Efficient Bound Tightening Techniques for Convex Relaxations of AC Optimal Power Flow

Shchetinin, Dmitry; Rubira, Tomás Tinoco De; Hug, Gabriela

doi:10.1109/tpwrs.2019.2905232

Cited by 23 publications

(20 citation statements)

References 21 publications

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“…The dataset creation method consists of several steps. First, all the upper and lower bounds in the AC-OPF problem and on the input variables in x are tightened using bound tightening algorithms in [38] and [39]. Second, relying on infeasibility certificates based on convex relaxations of the AC-OPF, large parts of the input space can be characterized as infeasible, i.e.…”

Section: E N-1 Security and Uncertaintymentioning

confidence: 99%

Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

Venzke

Chatzivasileiadis

2021

IEEE Trans. Smart Grid

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This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black box; this has presented a major barrier for their adoption in practice. Developing a rigorous framework based on mixed-integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe, and are able to systematically identify adversarial examples. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems. This paper presents the framework, methods to assess and improve neural network robustness in power systems, and addresses concerns related to scalability and accuracy. We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162bus systems, treating both N-1 security and small-signal stability.

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Section: E N-1 Security and Uncertaintymentioning

confidence: 99%

Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

Venzke

Chatzivasileiadis

2021

IEEE Trans. Smart Grid

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“…We note that the constraint sets C v , C θ , C p , C q , C s can be naively defined using the engineering constraints associated with whatever optimization problem the NN is ultimately being used to solve (e.g., UC, OPF, etc.). Alternatively, these constraint sets can themselves be first tightened using, e.g., optimization-based bound tightening [24] or analytic methods [25].…”

Section: Compression Of the Nn-based Power Flow Mappingmentioning

confidence: 99%

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Kody¹,

Chevalier²,

Chatzivasileiadis³

et al. 2021

Preprint

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Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem). Index Terms-AC power flow, AC unit commitment (AC-UC), mixed-integer linear program (MILP), neural networks, piecewise linear model I. INTRODUCTIONThe AC power flow equations are routinely used to model network constraints in optimization problems related to the control, operation, and planning of power systems. These constraints, however, are both nonlinear and non-convex, resulting in optimization problems that can be NP-hard [1]. In practice, many power systems operation problems, like unit commitment (UC), optimal power flow (OPF), and optimal transmission switching (OTS), are solved using linearized approximations of the nonlinear AC power flow equations for the sake of computational tractability. However, linear approximations can result in suboptimal solutions or solutions that are infeasible in the original, nonlinear problem [2].Piecewise linear models offer a method of improving solution accuracy by capturing some of the nonlinearity of the † denotes an equal contribution among authors.

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“…Constraint 20is considered to prevent the depletion of batteries over the planning horizon. The relations between maximum available powers, as uncertain parameters determined in the second-level, with utilized generations and spillages are formulated in (21) and 22for wind and solar powers, respectively. Load curtailments are restricted to their corresponding loads in (23).…”

Section: Definition Of Feasibility Setsmentioning

confidence: 99%

Contingency‐constrained operation optimization of microgrid with wind and solar generations: A decision‐driven stochastic adaptive‐robust approach

Ebrahimi

Amjady

2021

IET Renewable Power Gen

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This paper presents a decision‐driven stochastic adaptive‐robust microgrid operation optimization model considering the uncertainties of wind and solar generations, electricity price, and demand as well as the availability uncertainties of microgrid's components. Unlike previous works, this paper utilizes stochastic adaptive‐robust optimization approach to model both continuous and binary uncertainties simultaneously. To do so, adaptive‐robust optimization is used to model the continuous uncertainties, while the binary uncertainties are modelled by means of stochastic programming. An operating dispatchable unit usually exhibits a higher forced outage rate than a de‐committed one. Hence, due to the effect of the optimization decisions on the availability uncertainties, this research work proposes an intrinsic scenario production technique to model these binary uncertainties. In addition, a tri‐level decomposition method is introduced to solve the proposed microgrid operation optimization problem. In this decomposition method, the worst‐case realization of continuous uncertain parameters and unit commitment decisions are determined at each iteration considering the produced scenarios in the previous iteration. Case studies on the IEEE 69‐bus test system exhibit the effectiveness of the proposed decision‐driven stochastic adaptive‐robust model and the proposed solution method.

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Efficient Bound Tightening Techniques for Convex Relaxations of AC Optimal Power Flow

Cited by 23 publications

References 21 publications

Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Contingency‐constrained operation optimization of microgrid with wind and solar generations: A decision‐driven stochastic adaptive‐robust approach

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