Structured nonconvex optimization of large-scale energy systems using PIPS-NLP

Chiang, Nai-Yuan; Petra, Cosmin G.; Zavala, Ví­ctor M.

doi:10.1109/pscc.2014.7038374

Cited by 46 publications

(45 citation statements)

References 12 publications

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“…There has been recently a lot of interest in the development of efficient methods for stochastic optimal control problems such as stochastic gradient methods [23], the alternating directions method of multipliers (ADMM) [24] and various decomposition methods which can lead to parallelizable methods [25,26] (the most popular being the stochastic dual approximate dynamic programming [27], the progressive hedging approach [28] and dynamic programming [29]). There have been proposed parallelizable interior point algorithms for two-stage stochastic optimal control problems such as [30,31,32,33] and an ad hoc interior point solver for multi-stage problems [34]. However, interior point algorithms involve complex steps and are not suitable for an implementation on GPUs which can make the most of the capabilities of the hardware.…”

Section: State Of the Artmentioning

confidence: 99%

Uncertainty-aware demand management of water distribution networks in deregulated energy markets

Sopasakis¹,

Sampathirao²,

Bemporad³

et al. 2018

Environmental Modelling & Software

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We present an open-source solution for the operational control of drinking water distribution networks which accounts for the inherent uncertainty in water demand and electricity prices in the day-ahead market of a volatile deregulated economy. As increasingly more energy markets adopt this trading scheme, the operation of drinking water networks requires uncertainty-aware control approaches that mitigate the effect of volatility and result in an economic and safe operation of the network that meets the consumers' need for uninterrupted water supply. We propose the use of scenario-based stochastic model predictive control: an advanced control methodology which comes at a considerable computation cost which is overcome by harnessing the parallelization capabilities of graphics processing units (GPUs) and using a massively parallelizable algorithm based on the accelerated proximal gradient method.

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Section: State Of the Artmentioning

confidence: 99%

Uncertainty-aware demand management of water distribution networks in deregulated energy markets

Sopasakis¹,

Sampathirao²,

Bemporad³

et al. 2018

Environmental Modelling & Software

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“…When we are interested in finding local solutions , one can use an interior point solver and exploit the underlying linear algebra when computing Newton (search) steps . It is well‐known that the linear algebra system of problem (0.16) (a similar approach can be applied to (0.17)) can be permuted to the following block‐bordered‐diagonal (BBD) form:

true[\begin{matrix} K_{π} & B_{1}^{T} & B_{2}^{T} & \dots & B_{| Ω |}^{T} \\ B_{1} & K_{1} \\ B_{2} & K_{2} \\ ⋮ & ⋱ \\ B_{| Ω |} & K_{| Ω |} \end{matrix} true] true[\begin{matrix} Δ w_{π} \\ Δ w_{1} \\ Δ w_{2} \\ ⋮ \\ Δ w_{| Ω |} \end{matrix} true] = - true[\begin{matrix} r_{π} \\ r_{1} \\ r_{2} \\ ⋮ \\ r_{| Ω |} \end{matrix} true],

where

Δ w_{π} = (Δ π, Δ {normalλ}_{π}), Δ w_{ξ} = (Δ y_{ξ}, Δ {normalλ}_{ξ})

are the Newton steps,

K_{π} = W_{π}

K_{ξ} = true[\begin{matrix} W_{ξ} & J_{ξ}^{T} \\ J_{ξ} \end{matrix} true],

...…”

Section: Computational Toolsmentioning

confidence: 99%

“…To do this, it leverages a hierarchical graph abstraction wherein nodes and edges can be associated with individual JuMP scenario problems that are linked together (e.g., by using non‐anticipativity constraints) . Given a graph structure with models and connections, Plasmo can produce either a pure (flattened) optimization model to be solved using off‐the‐shelf optimization solvers such as IPOPT or it can communicate graph structures to structure‐exploiting solvers such as PIPS‐NLP and SNGO . Modeling and solution capabilities for stochastic programs are also provided by the popular Python‐based package PySP …”

Section: Computational Toolsmentioning

confidence: 99%

Optimal PID controller tuning using stochastic programming techniques

et al. 2017

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We argue that stochastic programming provides a powerful framework to tune and analyze the performance limits of controllers. In particular, stochastic programming formulations can be used to identify controller settings that remain robust across diverse scenarios (disturbances, set-points, and modeling errors) observed in real-time operations. We also discuss how to use historical data and sampling techniques to construct operational scenarios and inference analysis techniques to provide statistical guarantees on limiting controller performance. Under the proposed framework, it is also possible to use risk metrics to handle extreme (rare) events and stochastic dominance concepts to conduct systematic benchmarking studies. We provide numerical studies to illustrate the concepts and to demonstrate that modern modeling and local/global optimization tools can tackle large-scale applications. The proposed work also opens the door to data-based controller tuning strategies that can be implemented in real-time operations. V C 2017 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2017

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“…We solved the coupled and uncoupled models using a 24-hour time horizon with 1-hour time resolu- We solve the NLP using the interior-point optimization solver PIPS-NLP [9], which uses the filter line-search algorithm implemented in IPOPT [22]. PIPS-NLP is used to experiment with different linear algebra solvers and modeling interfaces.…”

Section: Model Solutionmentioning

confidence: 99%

Large-scale optimal control of interconnected natural gas and electrical transmission systems

Chiang

Zavala

2016

Applied Energy

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We present a detailed optimal control model that captures spatiotemporal interactions between gas and electric transmission networks. We use the model to study flexibility and economic opportunities provided by coordination. A large-scale case study in the Illinois system reveals that coordination can enable the delivery of significantly larger amounts of natural gas to the power grid. In particular, under a coordinated setting, gas-fired generators act as distributed demand response resources that can be controlled by the gas pipeline operator. This enables more efficient control of pressures and flows in space and time and overcomes delivery bottlenecks. We demonstrate that the additional flexibility not only can benefit the gas operator but can also lead to more efficient power grid operations and results in increased revenue for gas-fired power plants. We also use the optimal control model to analyze computational issues arising in these complex models. We demonstrate that the interconnected Illinois system with full physical resolution gives rise to a highly nonlinear optimal control problem with 4,400 differential and algebraic equations and 1,040 controls that can be solved with a state-of-the-art sparse optimization solver.

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Structured nonconvex optimization of large-scale energy systems using PIPS-NLP

Cited by 46 publications

References 12 publications

Uncertainty-aware demand management of water distribution networks in deregulated energy markets

Uncertainty-aware demand management of water distribution networks in deregulated energy markets

Optimal PID controller tuning using stochastic programming techniques

Large-scale optimal control of interconnected natural gas and electrical transmission systems

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