The Price of Uncertainty: Chance-Constrained OPF vs. in-Hindsight OPF

Muhlpfordt, Tillodont; Hagenmeyer, Veit; Faulwasser, Timm

doi:10.23919/pscc.2018.8442162

Cited by 6 publications

(10 citation statements)

References 33 publications

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“…Put differently, at the present stage it is unclear how to design stochastic nmpc for multi-stage ac opf such that the power-flow constraints are viably satisfied. Even in the single-stage case it is not yet clear how to transfer the dc results on viable formulations of [75,76] to the ac setting. Finally, it is also worth investigating how to solve sopf in distributed fashion.…”

Section: Stochastic and Distributed Opfmentioning

confidence: 99%

Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

Faulwasser

Engelmann

Mühlpfordt

et al. 2018

At - Automatisierungstechnik

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The Energiewende is a paradigm change that can be witnessed at latest since the political decision to step out of nuclear energy. Moreover, despite common roots in Electrical Engineering, the control community and the power systems community face a lack of common vocabulary. In this context, this paper aims at providing a systems-and-control specific introduction to optimal power flow problems which are pivotal in the operation of energy systems. Based on a concise problem statement, we introduce a common description of optimal power flow variants including multi-stage-problems and predictive control, stochastic uncertainties, and issues of distributed optimization. Moreover, we sketch open questions that might be of interest for the systems and control community.

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Section: Stochastic and Distributed Opfmentioning

confidence: 99%

Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

Faulwasser

Engelmann

Mühlpfordt

et al. 2018

At - Automatisierungstechnik

Self Cite

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“…with γ 1 = ψ 1 , ψ 1 = 2 35 B(4,2) , where B(·, ·) is the Beta function. Having solved (36), the optimal PCE becomes u = u 0 + u 1 ψ 1 in terms of the stochastic germ ξ; see Table 1 for numerical values of the optimal PCE coefficients. For practical considerations the optimal feedback policy in terms of the uncertain demand d is of interest.…”

Section: Beta Distributionmentioning

confidence: 99%

“…The optimal PCE coefficients are the solution to the socp (30), from which optimal policies are recovered. 12 To assess the quality of the optimized policies via CC-OPF we compare them to the policies from the most-informative case, namely in-hindsight OPF (hOPF) [36]; in-hindsight policies are obtained by sampling the uncertainties, and then solving a deterministic OPF problem for every sample. 13 The policy from hOPF provides the best distribution of optimal inputs and satisfies the constraints strictly for every sample.…”

Section: -Bus Examplementioning

confidence: 99%

A generalized framework for chance-constrained optimal power flow

Mühlpfordt

Faulwasser

Hagenmeyer

2018

Sustainable Energy, Grids and Networks

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Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call-among others-for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to guarantee power balance while maintaining economic and secure operation. In the presence of Gaussian uncertainties affine feedback policies are known to be viable options for this task. The present paper advocates a general framework for chance-constrained OPF problems in terms of continuous random variables. It is shown that, irrespective of the type of distribution, the random-variable minimizers lead to affine feedback policies. Introducing a three-step methodology that exploits polynomial chaos expansion, the present paper provides a constructive approach to chance-constrained optimal power flow problems that does not assume a specific distribution, e.g. Gaussian, for the uncertainties. We illustrate our findings by means of a tutorial example and a 300-bus test case.

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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 Price of Uncertainty: Chance-Constrained OPF vs. in-Hindsight OPF

Cited by 6 publications

References 33 publications

Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

Optimal power flow: an introduction to predictive, distributed and stochastic control challenges

A generalized framework for chance-constrained optimal power flow

A Survey of Real-Time Optimal Power Flow

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