Stochastic optimal power flow based on convex approximations of chance constraints

Summers, Tyler H.; Warrington, Joseph; Morari, Manfred; Lygeros, John

doi:10.1109/pscc.2014.7038376

Cited by 42 publications

(28 citation statements)

References 10 publications

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“…However, robust optimization has only been applied to specific sub-problems in electricity market operation, e.g. the unit commitment problem of the system operator [29], [30], [31], [32], nonstrategic bidding as a price-taker [22], strategic equilibrium in a Stackelberg leader-follower game [33], and strategic equilibrium without congestion costs [34].…”

Section: A Relevant Literaturementioning

confidence: 99%

Robust Cournot-Bertrand equilibria on power networks

Mather

Munsing

2017

2017 American Control Conference (ACC)

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Abstract-We present a convex model describing risk-averse strategies for electricity producers in congested electricity networks. Extending prior work on Cournot-Bertrand equilibria in Poolco-style spot markets with locational marginal pricing, we propose a formulation which integrates uncertainty through robust convex optimization. We find that producers uniformly benefit from robust strategies under small uncertainty intervals, and explore the impacts of congestion and network effects on strategic behavior. We demonstrate our results on a simple example and explore the impacts of robust strategies on social welfare, finding that these risk-averse strategies reduce welfare by restricting output and increasing prices. By formulating the equilibrium conditions as a convex optimization problem, we are able to scale our results to large networks and accommodate many sources of uncertainty.

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Section: A Relevant Literaturementioning

confidence: 99%

Robust Cournot-Bertrand equilibria on power networks

Mather

Munsing

2017

2017 American Control Conference (ACC)

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“…The required uncertainty intervals are derived either from a price forecasting model or as a percentage around the expected value, if such a model is not available. Even though RO can capture to some extent time dependencies between uncertain variables and expand the scenario set into consideration, it can lead to very conservative policies by enforcing feasibility constraints for each scenario and adapt the optimal decisions to the worst-case scenarios [8]- [9].…”

Section: A Backgroundmentioning

confidence: 99%

A stochastic dual dynamic programming approach for optimal operation of DER aggregators

Fatouros

Konstantelos

Papadaskalopoulos

et al. 2017

2017 IEEE Manchester PowerTech

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Abstract-The operation of aggregators of distributed energy resources (DER) is a highly complex task that is affected by numerous factors of uncertainty such as renewables injections, load levels and market conditions. However, traditional stochastic programming approaches neglect information around temporal dependency of the uncertain variables due to computational tractability limitations. This paper proposes a novel stochastic dual dynamic programming (SDDP) approach for the optimal operation of a DER aggregator. The traditional SDDP framework is extended to capture temporal dependency of the uncertain wind power output, through the integration of an n-order autoregressive (AR) model. This method is demonstrated to achieve a better trade-off between solution efficiency and computational time requirements compared to traditional stochastic programming approaches based on the use of scenario trees.

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“…[3]- [11], but only few have considered the application of corrective control actions or the existence of power flow control devices such as PSTs or HVDC. In [12], [13], a threestage optimal power flow (OPF) framework where corrective control actions are used to ensure feasibility during worst-case combinations of contingencies and uncertainty was proposed, and was extended to the definition of optimal corrective control actions in [14].…”

Section: Introductionmentioning

confidence: 99%

Corrective control to handle forecast uncertainty: A chance constrained optimal power flow

Roald

Misra

Krause

et al. 2017

2017 IEEE Manchester PowerTech

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Abstract-Higher shares of electricity generation from renewable energy sources and market liberalization is increasing uncertainty in power systems operation. At the same time, operation is becoming more flexible with improved control systems and new technology such as phase shifting transformers (PSTs) and high voltage direct current connections (HVDC). Previous studies have shown that the use of corrective control in response to outages contributes to a reduction in operating cost, while maintaining N-1 security. In this work, we propose a method to extend the use of corrective control of PSTs and HVDCs to react to uncertainty. We characterize the uncertainty as continuous random variables, and define the corrective control actions through affine control policies. This allows us to efficiently model control reactions to a large number of uncertainty sources. The control policies are then included in a chance constrained optimal power flow formulation, which guarantees that the system constraints are enforced with a desired probability. By applying an analytical reformulation of the chance constraints, we obtain a second-order cone problem for which we develop an efficient solution algorithm. In a case study for the IEEE 118 bus system, we show that corrective control for uncertainty leads to a decrease in operational cost, while maintaining system security. Further, we demonstrate the scalability of the method by solving the problem for the IEEE 300 bus and the Polish system test cases.

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Stochastic optimal power flow based on convex approximations of chance constraints

Cited by 42 publications

References 10 publications

Robust Cournot-Bertrand equilibria on power networks

Robust Cournot-Bertrand equilibria on power networks

A stochastic dual dynamic programming approach for optimal operation of DER aggregators

Corrective control to handle forecast uncertainty: A chance constrained optimal power flow

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