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Relevant bibliographies by topics / Security-Constrained Optimal Power Flow

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Academic literature on the topic 'Security-Constrained Optimal Power Flow'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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Journal articles on the topic "Security-Constrained Optimal Power Flow"

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Thomas, James Jamal, and Santiago Grijalva. "Flexible Security-Constrained Optimal Power Flow." IEEE Transactions on Power Systems 30, no. 3 (May 2015): 1195–202. http://dx.doi.org/10.1109/tpwrs.2014.2345753.

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Harsan, H., N. Hadjsaid, and P. Pruvot. "Cyclic security analysis for security constrained optimal power flow." IEEE Transactions on Power Systems 12, no. 2 (May 1997): 948–53. http://dx.doi.org/10.1109/59.589787.

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Fu, Cong, Yashan Zhong, Pingping Zhang, Xiangzhen He, Yun Yang, and Jian Zuo. "VSC-HVDC Incorporated Corrective Security-Constrained Optimal Power Flow." Journal of Physics: Conference Series 2320, no. 1 (August 1, 2022): 012006. http://dx.doi.org/10.1088/1742-6596/2320/1/012006.

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Abstract With the rapid development and diverse engineering applications of VSC-HVDC technology, development in power industry has put forward higher economic and security requirements for the security-constrained optimal power flow. Under these circumstances, this paper proposes a security-constrained optimal power flow model for hybrid AC/DC power grids that incorporates the VSC-HVDC corrective control. The linear relationship between the pre-contingency state power flow and post-contingency state power flow is established based on the shift factor and the reliability constraints are described as the linear inequality constraints of the post-contingency state active power flow which is expressed by the pre-contingency state branch power flow. With the inherent ability of the VSC-HVDC converter station (short as VSC station) to rapidly regulate active power taken into account, this paper utilizes the linear relationship between the active power adjustment of the VSC station and the power flows of transmission lines and electrical equipment and corrects the reliability constraints with the sensitivity coefficient. Hence the correction of the post-contingency state power flow is reflected in the constraints. By solving the proposed model with the primal-dual interior-point method, the pre-contingency state optimal security operating point that considers the corrective capability of the VSC stations is obtained. Finally, the correctness and validity of the proposed model is verified based on a VSC-HVDC modified IEEE 14-bus system.

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Mohammadi, Javad, Gabriela Hug, and Soummya Kar. "Agent-Based Distributed Security Constrained Optimal Power Flow." IEEE Transactions on Smart Grid 9, no. 2 (March 2018): 1118–30. http://dx.doi.org/10.1109/tsg.2016.2577684.

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Gutierrez-Martinez, Victor J., Claudio A. Canizares, Claudio R. Fuerte-Esquivel, Alejandro Pizano-Martinez, and Xueping Gu. "Neural-Network Security-Boundary Constrained Optimal Power Flow." IEEE Transactions on Power Systems 26, no. 1 (February 2011): 63–72. http://dx.doi.org/10.1109/tpwrs.2010.2050344.

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Correa-Posada, Carlos M., and Pedro Sanchez-Martin. "Security-Constrained Optimal Power and Natural-Gas Flow." IEEE Transactions on Power Systems 29, no. 4 (July 2014): 1780–87. http://dx.doi.org/10.1109/tpwrs.2014.2299714.

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Somasundaram, P., K. Kuppusamy, and R. P. Kumudini Devi. "Evolutionary programming based security constrained optimal power flow." Electric Power Systems Research 72, no. 2 (December 2004): 137–45. http://dx.doi.org/10.1016/j.epsr.2004.02.006.

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Vaahedi, E., Y. Mansour, C. Fuchs, S. Granville, M. D. L. Latore, and H. Hamadanizadeh. "Dynamic security constrained optimal power flow/VAr planning." IEEE Transactions on Power Systems 16, no. 1 (2001): 38–43. http://dx.doi.org/10.1109/59.910779.

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Binkou, Alhabib, and Yixin Yu. "Security constrained distributed optimal power flow of interconnected power systems." Transactions of Tianjin University 14, no. 3 (June 2008): 208–16. http://dx.doi.org/10.1007/s12209-008-0038-2.

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Li, Hang, Zhe Zhang, Xianggen Yin, and Buhan Zhang. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees." Energies 13, no. 9 (May 8, 2020): 2344. http://dx.doi.org/10.3390/en13092344.

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The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energy sources (RES) and loads, the existing SCOPF model has difficulty meeting the practical requirements of the industry. This paper proposed a novel chance-constrained preventive SCOPF model that considers the uncertainty of power injections, including RES and load, and contingency probability. The chance constraint is used to constrain the overall line flow within the limits with high probabilistic guarantees and to significantly reduce the constraint scales. The cumulant and Johnson systems were combined to accurately approximate the cumulative distribution functions, which is important in solving chance-constrained optimization problems. The simulation results show that the model proposed in this paper can achieve better performance than traditional SCOPF.

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Dissertations / Theses on the topic "Security-Constrained Optimal Power Flow"

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Zhang, Fan. "Solving Large Security-Constrained Optimal Power Flow for Power Grid Planning and Operations." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1592567584117811.

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Chiang, Naiyuan. "Structure-exploiting interior point methods for security constrained optimal power flow problems." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8281.

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The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods (IPM). Firstly, we consider a DC-SCOPF model, which is a linearized version of AC-SCOPF. One new reformulation of the DC-SCOPF model is suggested, in which most matrices that need to be factorized are constant. Consequently, most numerical factorizations and a large number of back-solve operations only need to be performed once throughout the entire IPM process. In the framework of the structure-exploiting IPM implementation, one of the major computational efforts consists of forming the Schur complement matrix, which is very computationally expensive if no further measure is applied. One remedy is to apply a preconditioned iterative method to solve the corresponding linear systems which appear in assembling the Schur complement matrix. We suggest two main schemes to pick a good and robust preconditioner for SCOPF problems based on combining different “active” contingency scenarios. The numerical results show that our new approaches are much faster than the default structure-exploiting method in OOPS, and also that it requires less memory. The second part of this thesis goes to the standard AC-SCOPF problem, which is a nonlinear and nonconvex optimization problem. We present a new contingency generation algorithm: it starts with solving the basic OPF problem, which is a much smaller problem of the same structure, and then generates contingency scenarios dynamically when needed. Some theoretical analysis of this algorithm is shown for the linear case, while the numerical results are exciting, as this new algorithm works for both AC and DC cases. It can find all the active scenarios and significantly reduce the number of scenarios one needs to contain in the model. As a result, it speeds up the solving process and may require less IPM iterations. Also, some heuristic algorithms are designed and presented to predict the active contingencies for the standard AC-SCOPF, based on the use of AC-OPF or DC-SCOPF. We test our heuristic algorithms on the modified IEEE 24-bus system, and also present their corresponding numerical results in the thesis.

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Zhang, Shouming. "Security optimised optimal power flow." Thesis, Brunel University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320858.

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Bahrami, Shahab. "Algorithm design for optimal power flow, security-constrained unit commitment, and demand response in energy systems." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62754.

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Energy management is of prime importance for power system operators to enhance the use of the existing and new facilities, while maintaining a high level of reliability. In this thesis, we develop analytical models and efficient algorithms for energy management programs in transmission and distribution networks. First, we study the optimal power flow (OPF) in ac-dc grids, which is a non-convex optimization problem. We use convex relaxation techniques and transform the problem into a semidefinite program (SDP). We derive the sufficient conditions for zero relaxation gap and design an algorithm to obtain the global optimal solution. Subsequently, we study the security-constrained unit commitment (SCUC) problem in ac-dc grids with generation and load uncertainty. We introduce the concept of conditional value-at risk to limit the net power supply shortage. The SCUC is a nonlinear mixed-integer optimization problem. We use ℓ₁-norm approximation and convex relaxation techniques to transform the problem into an SDP. We develop an algorithm to determine a near-optimal solution. Next, we target the role of end-users in energy management activities. We study demand response programs for residential users and data centers. For residential users, we capture their coupled decision making in a demand response program with real-time pricing as a partially observable stochastic game. To make the problem tractable, we approximate the optimal scheduling policy of the residential users by the Markov perfect equilibrium (MPE) of a fully observable stochastic game with incomplete information. We develop an online load scheduling learning algorithm to determine the users’ MPE policy. Last but not least, we focus on the demand response program for data centers in deregulated electricity markets, where each data center can choose a utility company from multiple available suppliers. We model the data centers’ coupled decisions of utility company choices and workload scheduling as a many-to-one matching game with externalities. We characterize the stable outcome of the game, where no data center has an incentive to unilaterally change its strategy. We develop a distributed algorithm that is guaranteed to converge to a stable outcome.
Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate

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Pajic, Slobodan. "Sequential quadratic programming-based contingency constrained optimal power flow." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0430103-152758.

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Mohammadi, Javad. "Distributed Computational Methods for Energy Management in Smart Grids." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/710.

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It is expected that the grid of the future differs from the current system by the increased integration of distributed generation, distributed storage, demand response, power electronics, and communications and sensing technologies. The consequence is that the physical structure of the system becomes significantly more distributed. The existing centralized control structure is not suitable any more to operate such a highly distributed system. This thesis is dedicated to providing a promising solution to a class of energy management problems in power systems with a high penetration of distributed resources. This class includes optimal dispatch problems such as optimal power flow, security constrained optimal dispatch, optimal power flow control and coordinated plug-in electric vehicles charging. Our fully distributed algorithm not only handles the computational complexity of the problem, but also provides a more practical solution for these problems in the emerging smart grid environment. This distributed framework is based on iteratively solving in a distributed fashion the first order optimality conditions associated with the optimization formulations. A multi-agent viewpoint of the power system is adopted, in which at each iteration, every network agent updates a few local variables through simple computations, and exchanges information with neighboring agents. Our proposed distributed solution is based on the consensus+innovations framework, in which the consensus term enforces agreement among agents while the innovations updates ensure that local constraints are satisfied.

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Macfie, Peter. "Large-scale security constrained optimal reactive power flow for operational loss management on the GB electricity transmission network." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/5073.

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The transmission of power across the GB transmission system, as operated by National Grid, results in inevitable loss of electrical power. Operationally these power losses cannot be eliminated, but they can be reduced by adjustment of the system voltage profile. At present the minimisation of active power losses relies upon a lengthy manually based iterative adjustment process. Therefore the system operator requires the development of advanced optimisation tools to cope with the challenges faced over the next decade, such as achieving the stringent greenhouse gas emission targets laid down by the UK government, while continue to provide an economical, secure and efficient service. To meet these challenges the research presented in this thesis has developed optimisation techniques that can assist control centre engineers by automatically setting up voltage studies that are low loss and low cost. The proposed voltage optimisation techniques have been shown to produce solutions that are secured against 800 credible contingency cases. A prototype voltage optimisation tool has been deployed, which required the development of a series of novel approaches to extend the functionality of an existing optimisation program. This research has lead to the development of novel methods for handling multi-objectives, contradictory shunt switching configurations and selecting all credible contingencies. Studies indicate that a theoretical loss saving of 1.9% is achievable, equivalent to an annual emissions saving of approximately 64,000 tonnes of carbon dioxide. A novel security constrained mixed integer non-linear optimisation technique has also been developed. The proposed method has been shown to be superior to several conventional methods on a wide range of IEEE standard network models and also on a range of large-scale GB network models. The proposed method manages to further reduce active power losses and also satisfies all security constraints.

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8

Hamon, Camille. "Probabilistic security management for power system operations with large amounts of wind power." Doctoral thesis, KTH, Elektriska energisystem, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-166398.

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Power systems are critical infrastructures for the society. They are therefore planned and operated to provide a reliable eletricity delivery. The set of tools and methods to do so are gathered under security management and are designed to ensure that all operating constraints are fulfilled at all times. During the past decade, raising awareness about issues such as climate change, depletion of fossil fuels and energy security has triggered large investments in wind power. The limited predictability of wind power, in the form of forecast errors, pose a number of challenges for integrating wind power in power systems. This limited predictability increases the uncertainty already existing in power systems in the form of random occurrences of contingencies and load forecast errors. It is widely acknowledged that this added uncertainty due to wind power and other variable renewable energy sources will require new tools for security management as the penetration levels of these energy sources become significant. In this thesis, a set of tools for security management under uncertainty is developed. The key novelty in the proposed tools is that they build upon probabilistic descriptions, in terms of distribution functions, of the uncertainty. By considering the distribution functions of the uncertainty, the proposed tools can consider all possible future operating conditions captured in the probabilistic forecasts, as well as the likeliness of these operating conditions. By contrast, today's tools are based on the deterministic N-1 criterion that only considers one future operating condition and disregards its likelihood. Given a list of contingencies selected by the system operator and probabilitistic forecasts for the load and wind power, an operating risk is defined in this thesis as the sum of the probabilities of the pre- and post-contingency violations of the operating constraints, weighted by the probability of occurrence of the contingencies. For security assessment, this thesis proposes efficient Monte-Carlo methods to estimate the operating risk. Importance sampling is used to substantially reduce the computational time. In addition, sample-free analytical approximations are developed to quickly estimate the operating risk. For security enhancement, the analytical approximations are further embedded in an optimization problem that aims at obtaining the cheapest generation re-dispatch that ensures that the operating risk remains below a certain threshold. The proposed tools build upon approximations, developed in this thesis, of the stable feasible domain where all operating constraints are fulfilled.

QC 20150508

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Pajic, Slobodan. "Power System State Estimation and Contingency Constrained Optimal Power Flow - A Numerically Robust Implementation." Digital WPI, 2007. https://digitalcommons.wpi.edu/etd-dissertations/240.

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The research conducted in this dissertation is divided into two main parts. The first part provides further improvements in power system state estimation and the second part implements Contingency Constrained Optimal Power Flow (CCOPF) in a stochastic multiple contingency framework. As a real-time application in modern power systems, the existing Newton-QR state estimation algorithms are too slow and too fragile numerically. This dissertation presents a new and more robust method that is based on trust region techniques. A faster method was found among the class of Krylov subspace iterative methods, a robust implementation of the conjugate gradient method, called the LSQR method. Both algorithms have been tested against the widely used Newton-QR state estimator on the standard IEEE test networks. The trust region method-based state estimator was found to be very reliable under severe conditions (bad data, topological and parameter errors). This enhanced reliability justifies the additional time and computational effort required for its execution. The numerical simulations indicate that the iterative Newton-LSQR method is competitive in robustness with classical direct Newton-QR. The gain in computational efficiency has not come at the cost of solution reliability. The second part of the dissertation combines Sequential Quadratic Programming (SQP)-based CCOPF with Monte Carlo importance sampling to estimate the operating cost of multiple contingencies. We also developed an LP-based formulation for the CCOPF that can efficiently calculate Locational Marginal Prices (LMPs) under multiple contingencies. Based on Monte Carlo importance sampling idea, the proposed algorithm can stochastically assess the impact of multiple contingencies on LMP-congestion prices.

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Zhang, Wang. "Optimisation and Integration of Variable Renewable Energy Sources in Electricity Networks." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16858.

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The growing penetration of renewable energy sources (RESs) into the electricity power grid is profitable from a sustainable point of view and provides economic benefit for long-term operation. Nevertheless, balancing production and consumption is and will always be a crucial requirement for power system operation. However, the trend towards increasing RESs penetration has raised concerns about the stability, reliability and security of future electricity grids. The clearest observation in this regard is the intermittent nature of RESs. Moreover, the location of renewable generation tends to be heavily defined by meteorological and geographical conditions, which makes the generation sites distant from load centres. These facts make the analysis of electricity grid operation under both dynamic and the steady state more difficult, posing challenges in effectively integrating variable RESs into electricity networks. The thesis reports on studies that were conducted to design efficient tools and algorithms for system operators, especially transmission system operators for reliable short-term system operation that accounts for intermittency and security requirements. Initially, the impact of renewable generation on the steady state is studied in the operation stage. Then, based on the first study, more sophisticated modeling on the electricity network are investigated in the third and fourth chapters. Extending the previous studies, the fourth chapter explores the potential of using multiple microgrids to support the main grid’s security control. Finally, the questions regarding the computational efficiency and convergence analysis are addressed in chapter 5 and a DSM model in a real-time pricing environment is introduced. This model presents an alternative way of using flexibility on the demand side to compensate for the uncertainties on the generation side.

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Book chapters on the topic "Security-Constrained Optimal Power Flow"

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Velay, Maxime, Meritxell Vinyals, Yvon Bésanger, and Nicolas Retière. "Agent-Based Security Constrained Optimal Power Flow with Primary Frequency Control." In Multi-Agent Systems and Agreement Technologies, 79–95. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01713-2_7.

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Xiaoqin, Xia, Xu Wei, Yuan Zhen, and Xu Xiaotong. "Parallel Decomposition and Coordination Algorithm for Security Constrained Optimal Power Flow." In Lecture Notes in Electrical Engineering, 107–16. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-7156-2_8.

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Somasundaram, P., and N. B. Muthuselvan. "Security Constrained Optimal Power Flow with FACTS Devices Using Modified Particle Swarm Optimization." In Swarm, Evolutionary, and Memetic Computing, 639–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-17563-3_75.

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Fioretto, Ferdinando, and Pascal Van Hentenryck. "Constrained-Based Differential Privacy: Releasing Optimal Power Flow Benchmarks Privately." In Integration of Constraint Programming, Artificial Intelligence, and Operations Research, 215–31. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93031-2_15.

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Rathod, Darshan B., and Rinkesh A. Jain. "Comparative Analysis on Security-Constrained Optimal Power Flow Using Linear Sensitivity Factors-Based Contingency Screening." In Advances in Intelligent Systems and Computing, 139–47. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1966-2_12.

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Devesh Raj, Mani, and Periyasami Somasundaram. "Small Signal Stability Constrained Optimal Power Flow Using Swarm Based Algorithm." In Swarm, Evolutionary, and Memetic Computing, 699–709. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03753-0_62.

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Huebner, Nico, Nils Schween, Michael Suriyah, Vincent Heuveline, and Thomas Leibfried. "Multi-area Coordination of Security-Constrained Dynamic Optimal Power Flow in AC-DC Grids with Energy Storage." In Trends in Mathematics, 27–40. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32157-4_3.

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Liu, Shichuan, Teng Mu, and Aijun Zhang. "Optimal Power Flow Calculation of Power System Based on Vector Distance Immune Algorithm." In The 2021 International Conference on Machine Learning and Big Data Analytics for IoT Security and Privacy, 815–21. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89508-2_106.

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Nithya, C., J. Preetha Roselyn, D. Devaraj, and Subhransu Sekhar Dash. "Voltage Stability Constrained Optimal Power Flow Using Non-dominated Sorting Genetic Algorithm-II (NSGA II)." In Swarm, Evolutionary, and Memetic Computing, 793–801. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-35380-2_93.

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Mahapatra, Sheila, Nitin Malik, and A. N. Jha. "Cuckoo Search Algorithm and Ant Lion Optimizer for Optimal Allocation of TCSC and Voltage Stability Constrained Optimal Power Flow." In International Conference on Intelligent Computing and Smart Communication 2019, 889–905. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0633-8_92.

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Conference papers on the topic "Security-Constrained Optimal Power Flow"

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Vrakopoulou, Maria, Marina Katsampani, Kostas Margellos, John Lygeros, and Goran Andersson. "Probabilistic security-constrained AC optimal power flow." In 2013 IEEE Grenoble PowerTech. IEEE, 2013. http://dx.doi.org/10.1109/ptc.2013.6652374.

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Rahman, Jubeyer, Cong Feng, and Jie Zhang. "Machine Learning-Aided Security Constrained Optimal Power Flow." In 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2020. http://dx.doi.org/10.1109/pesgm41954.2020.9281941.

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Zhong, Chiyang, A. P. Sakis Meliopoulos, Maad AlOwaifeer, Jiahao Xie, and Gad Ilunga. "Object-Oriented Security Constrained Quadratic Optimal Power Flow." In 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2020. http://dx.doi.org/10.1109/pesgm41954.2020.9282106.

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Mohammadi, Javad, Soummya Kar, and Gabriela Hug. "Fully distributed corrective security constrained optimal power flow." In 2017 IEEE Manchester PowerTech. IEEE, 2017. http://dx.doi.org/10.1109/ptc.2017.7981066.

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Canizares, C., W. Rosehart, A. Berizzi, and C. Bovo. "Comparison of voltage security constrained optimal power flow techniques." In Proceedings of Power Engineering Society Summer Meeting. IEEE, 2001. http://dx.doi.org/10.1109/pess.2001.970328.

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Chakrabarti, Sambuddha, Matt Kraning, Eric Chu, Ross Baldick, and Stephen Boyd. "Security Constrained Optimal Power Flow via proximal message passing." In 2014 Clemson University Power Systems Conference (PSC). IEEE, 2014. http://dx.doi.org/10.1109/psc.2014.6808131.

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Vahedi, H., S. H. Hosseini, and R. Noroozian. "Bacterial Foraging Algorithm for security constrained optimal power flow." In 2010 7th International Conference on the European Energy Market (EEM 2010). IEEE, 2010. http://dx.doi.org/10.1109/eem.2010.5558709.

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Wibowo, Rony Seto, Rendhi Maulana, Annisaa Taradini, Feby A. Pamuji, Adi Soeprijanto, and Ontoseno Penangsang. "Quadratic programming approach for security constrained optimal power flow." In 2015 7th International Conference on Information Technology and Electrical Engineering (ICITEE). IEEE, 2015. http://dx.doi.org/10.1109/iciteed.2015.7408941.

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Triwijaya, Santi, Nurdin Sugiantoro, Yuli Prasetyo, Firdaus, Rony Seto Wibowo, and Ontoseno Penangsang. "Security Constrained Optimal Power Flow Considering Dynamic Line Rating." In 2018 10th International Conference on Information Technology and Electrical Engineering (ICITEE). IEEE, 2018. http://dx.doi.org/10.1109/iciteed.2018.8534755.

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Feng Dong. "Practical applications of Preventive Security Constrained Optimal Power Flow." In 2012 IEEE Power & Energy Society General Meeting. New Energy Horizons - Opportunities and Challenges. IEEE, 2012. http://dx.doi.org/10.1109/pesgm.2012.6344734.

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Reports on the topic "Security-Constrained Optimal Power Flow"

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Kim, Kibaek, Youngdae Kim, Daniel Maldonado, Michel Schanen, Victor Zavala, and Nai-Yuan Chiang. A Scalable Mixed-Integer Decomposition Method for Security-Constrained Optimal Power Flow with Complementarity Constraints. Office of Scientific and Technical Information (OSTI), November 2021. http://dx.doi.org/10.2172/1835277.

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Bienstock, Daniel, Michael Chertkov, and Sean Harnett. Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty. Office of Scientific and Technical Information (OSTI), September 2012. http://dx.doi.org/10.2172/1052351.

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