A generalized framework for chance-constrained optimal power flow

Mühlpfordt, Tillmann; Faulwasser, Timm; Hagenmeyer, Veit

doi:10.1016/j.segan.2018.08.002

Cited by 47 publications

(40 citation statements)

References 37 publications

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“…The order of PCE necessary for sufficient accuracy depends on the effective nonlinearity in the power flow equations. For example, in case of DC power flow, it is known that PCE with degree N d = 1 is exact [8]. The fact that in our experiments a PCE basis of degree 2 has a small error shows that a degree of 2 is enough to capture the level of nonlinearity of the AC power flow equations for typical levels of uncertainty.…”

Section: A Satisfaction Of Ac Power Flow Constraintsmentioning

confidence: 60%

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Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach

Mühlpfordt

Roald

Hagenmeyer

et al. 2019

IEEE Trans. Power Syst.

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As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chanceconstrained optimal power flow while explicitly considering the full nonlinear AC power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the AC power flow equations and on the accurate computation of moments of all random variables.

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Section: A Satisfaction Of Ac Power Flow Constraintsmentioning

confidence: 60%

“…Polynomial chaos has been applied previously to power system optimization. For stochastic OPF under the DC approximation it has been shown that PCE provides exact and tractable convex reformulations [8,22]. With AC equations, [23,24] apply polynomial chaos to formulate the problem.…”

Section: Introductionmentioning

confidence: 99%

Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach

Mühlpfordt

Roald

Hagenmeyer

et al. 2019

IEEE Trans. Power Syst.

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“…In particular, the distributions of the generation of renewable energy are non-Gaussian, e.g., wind energy is usually described by the beta distribution [158][159][160]. Based on the distribution function of the random penetration, chance constrained OPF [35,51,[161][162][163] aims at minimizing/maximizing an objective function, while satisfying certain constraints with a predefined probability level. For a chance-constrained OPF, if the model is linear, and the random variables are normally distributed, there exists an equivalent deterministic representation.…”

Section: Stochastic Emssmentioning

confidence: 99%

A Survey of Real-Time Optimal Power Flow

et al. 2018

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There has been a strong increase of penetration of renewable energies into power systems. However, the renewables pose new challenges for the operation of the networks. Particularly, wind power is intermittently fluctuating, and, therefore, the network operator has to fast update the operations correspondingly. This task should be performed by an online optimization. Therefore, real-time optimal power flow (RT-OPF) has become an attractive topic in recent years. This paper presents an overview of recent studies on RT-OPF under wind energy penetration, offering a critical review of the major advancements in RT-OPF. It describes the challenges in the realization of the RT-OPF and presents available approaches to address these challenges. The paper focuses on a number of topics which are reviewed in chronological order of appearance: offline energy management systems (EMSs) (deterministic and stochastic approaches) and real-time EMSs (constraint satisfaction-based and OPF-based methods). The particular challenges associated with the incorporation of battery storage systems in the networks are explored, and it is concluded that the current research on RT-OPF is not sufficient, and new solution approaches are needed.Energies 2018, 11, 3142 2 of 20 time. However, the incorporation of BSSs into the network leads to dynamic state operations and thus introduces dynamic model equations to the OPF, which makes the problem more complex to solve. This complexity is due to the fact that the dynamic optimization is described by differential/difference equations, whereas static optimization requires only algebraic equations [30].Another issue is that the REG rate is uncertain. It means their output cannot be forecasted accurately, and there may be discrepancies between the forecasted and actually realized values. The uncertainties can lead to constraint violations and thus safety problems if they are not handled properly. Therefore, deterministic OPF methods are not suitable for the real operation of the networks, or their solutions need further modifications before realization. Besides, owing to fast fluctuating REG, in particular wind power, the network operators need to fast update-i.e., in real-time-the operation strategies correspondingly, in order for the network to operate economically and in its feasible region. Therefore, the real-time energy management systems (RT-EMSs) have attracted increasing interest from many researchers. In this paper, we classify the RT-EMSs into two main categories: (1) constraint satisfaction-based RT-EMSs, and (2) OPF-based RT-EMSs. The former can satisfy the technical constraints of the network in real time, but the solutions may not be optimal. The latter provides optimal solutions in real time while satisfying the constraints. It is noted that the technical constraints could be different for these two categories, depending on the components of the network (details can be seen in Section 2).The remainder of the paper is organized as follows: Section 2 provides the general formulation of OPF...

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“…The method of Reference 15 can be difficult to implement depending on the form of the constraint. In contrast, the method of Reference 16 uses arbitrary non‐Gaussian distributions to determine a deterministic approximation of the chance constraint, and is more straightforward to implement. In Reference 17, under the assumptions of convex and affine relations for the chance constraint, a convex chance constraint approximation is constructed.…”

Section: Introductionmentioning

confidence: 99%

Method for solving chance constrained optimal control problems using biased kernel density estimators

Keil

Miller

Kumar³

et al. 2020

Optim Control Appl Methods

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SummaryA method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a nontrivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. Additionally, the method is tested on a complex chance constrained unmanned aerial vehicle problem. The results show that this new method can be used to reliably solve chance constrained optimal control problems.

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A generalized framework for chance-constrained optimal power flow

Cited by 47 publications

References 37 publications

Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach

Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach

A Survey of Real-Time Optimal Power Flow

Method for solving chance constrained optimal control problems using biased kernel density estimators

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