Numerical Simulation for Stochastic Transient Stability Assessment
TL;DR: In this paper, a stochastic power system model based on SDEs is proposed to take into account the uncertain factors such as load levels and system faults, and the concept of strong convergence is also introduced to evaluate their accuracy.
Abstract: There has been continuous development of techniques for assessing the transient stability of power systems in the uncertain environment. In this paper, a novel framework for stochastic transient stability assessment is proposed. The basic theory of stochastic calculus is first introduced to form the mathematical basis of the proposed approach. A stochastic power system model based on stochastic differential equations (SDEs) is proposed to take into account the uncertain factors such as load levels and system faults. We then present a detailed discussion on the numerical methods for solving SDEs. The stochastic Euler and Milstein schemes are introduced. The concept of strong convergence is also introduced to evaluate their accuracy. The proposed approach is tested with comprehensive case studies to validate its effectiveness.
Citations
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21 Jul 2013
TL;DR: The features that makes the Python language an adequate tool for research, massive numerical simulations and education are discussed and a variety of examples are provided to show the advanced features and the performance of the developed tool.
Abstract: This paper presents a power system analysis tool, called DOME, entirely based on Python scripting language as well as on public domain efficient C and Fortran libraries. The objects of the paper are twofold. First, the paper discusses the features that makes the Python language an adequate tool for research, massive numerical simulations and education. Then the paper describes the architecture of the developed software tool and provides a variety of examples to show the advanced features and the performance of the developed tool.
199 citations
Cites background from "Numerical Simulation for Stochastic..."
...Moreover, DOME includes the possibility to model and numerically integrate stochastic processes, such as the Wiener and the Orstein-Uhlenbeck processes, which have been proposed in the literature [23], [24]....
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TL;DR: In this article, a general approach to model power systems as continuous stochastic differential-algebraic equations is proposed, and a case study illustrating the proposed approach is provided based on the IEEE 145-bus 50-machine system.
Abstract: This paper proposes a systematic and general approach to model power systems as continuous stochastic differential-algebraic equations. With this aim, the paper provides a theoretical background on stochastic differential-algebraic equations and justifies the need for stochastic models in power system analysis. Then, the paper describes a general procedure to define stochastic dynamic models. Practical issues related to the numerical integration of the resulting power system model are also discussed. A case study illustrating the proposed approach is provided based on the IEEE 145-bus 50-machine system. The case study also illustrates and compares the reliability of the results obtained using stochastic and conventional probabilistic models.
186 citations
163 citations
TL;DR: A critical assessment and classification of the available probabilistic computational methods that have been applied to power system stability assessment (including small and large disturbance angular stability, voltage and frequency stability) is provided in this paper.
Abstract: The analysis of power systems with a significant share of renewable generation using probabilistic tools is essential to appropriately consider the impact that the variability and intermittency of the renewable generation has on the grid. This paper provides a critical assessment and classification of the available probabilistic computational methods that have been applied to power system stability assessment (including small and large disturbance angular stability, voltage and frequency stability). A probabilistic analysis framework with a state-of-the-art review of the existing literature in the area is presented comprising of a review of (i) input variable modelling, (ii) computational methods and (iii) presentation techniques for the output/results. The most widely used probabilistic methods in power system studies are presented with their specific application areas, advantages, and disadvantages. The purpose of this overview, classification, and assessment of the existing methods is to identify the most appropriate probabilistic methods to be used in their current forms, or suitably modified, for different types of stability studies of power systems containing renewable generation.
108 citations
TL;DR: In this paper, a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates for the grids' stability in the presence of variations in power injections, and for the grid's ability to withstand a bunch sources of faults is introduced.
Abstract: Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates for the grids’ stability in the presence of variations in power injections, and for the grids’ ability to withstand a bunch sources of faults. By this toolbox we can “offline” screen a wide range of contingencies or power injection profiles, without reassessing the system stability on a regular basis. In particular, we formulate and solve two novel robust stability and resiliency assessment problems of power grids subject to the uncertainty in equilibrium points and uncertainty in fault-on dynamics. Furthermore, we bring in the quadratic Lyapunov functions approach to transient stability assessment, offering real-time construction of stability/resiliency certificates and real-time stability assessment. The effectiveness of the proposed techniques is numerically illustrated on a number of IEEE test cases.
84 citations
References
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Book•
01 Jan 1994
TL;DR: In this article, the authors present a model for the power system stability problem in modern power systems based on Synchronous Machine Theory and Modelling, and a model representation of the synchronous machine representation in stability studies.
Abstract: Part I: Characteristics of Modern Power Systems. Introduction to the Power System Stability Problem. Part II: Synchronous Machine Theory and Modelling. Synchronous Machine Parameters. Synchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems. High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Machine Representation in Stability Studies. AC Transmission. Power System Loads. Excitation in Stability Studies. Prime Mover and Energy Supply Systems, High-Voltage Direct-Current Transmission. Control of Active Power and Reactive Power. Part III: Small Signal Stability. Transient Stability. Voltage Stability. Subsynchronous Oscillations. Mid-Term and Long-Term Stability. Methods of Improving System Stability.
13,467 citations
"Numerical Simulation for Stochastic..." refers methods in this paper
...A widely used TSA method is time-domain simulation (TDS) [1]–[4]....
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Book•
01 Jun 1992
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Abstract: 1 Probability and Statistics- 2 Probability and Stochastic Processes- 3 Ito Stochastic Calculus- 4 Stochastic Differential Equations- 5 Stochastic Taylor Expansions- 6 Modelling with Stochastic Differential Equations- 7 Applications of Stochastic Differential Equations- 8 Time Discrete Approximation of Deterministic Differential Equations- 9 Introduction to Stochastic Time Discrete Approximation- 10 Strong Taylor Approximations- 11 Explicit Strong Approximations- 12 Implicit Strong Approximations- 13 Selected Applications of Strong Approximations- 14 Weak Taylor Approximations- 15 Explicit and Implicit Weak Approximations- 16 Variance Reduction Methods- 17 Selected Applications of Weak Approximations- Solutions of Exercises- Bibliographical Notes
6,284 citations
"Numerical Simulation for Stochastic..." refers background or methods in this paper
...The stochastic integral can be easily calculated as discussed in [19] and [23]....
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...To determine the accuracy of a discrete time approximation, we introduce the following definition [23]....
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...Similarly, by including higher order terms of the Itô-Taylor expansion, we can obtain other numerical schemes with higher convergence orders such as the Milstein scheme [23]...
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...Based on Definition 6, we can define the concept of strong convergence [23] as follows....
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...0 strong Taylor schemes as discussed in [19] and [23]....
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Book•
01 Jan 1990
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Abstract: I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential Equations.- VI Expansion of Filtrations.- References.
5,254 citations
"Numerical Simulation for Stochastic..." refers background in this paper
...A generalized definition of the Itô integral with respect to other stochastic processes can be found in [19] and [20]....
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TL;DR: In this article, a simple dynamic load model is proposed which captures the usual nonlinear steady-state behavior plus load recovery and overshoot, and a simple but important dynamic voltage stability analysis is developed based on the model.
Abstract: Motivated by projects in Sweden on voltage stability analysis and associated load modeling, a simple dynamic load model is proposed which captures the usual nonlinear steady-state behavior plus load recovery and overshoot. The parameters of the model can be related to physical devices depending on the time zone following a disturbance. A simple but important dynamic voltage stability analysis is developed based on the model. >
450 citations
"Numerical Simulation for Stochastic..." refers methods in this paper
...In this paper, we propose a modified exponential recovery load model [21], [22] based on SDEs....
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Book•
01 Jan 1996
TL;DR: An Introduction to the Mathematics of Financial Derivatives as mentioned in this paper is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus.
Abstract: An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems.Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learningPresented intuitively, breaking up complex mathematics concepts into easily understood notionsEncourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching
419 citations
"Numerical Simulation for Stochastic..." refers methods in this paper
...Two important stochastic processes will be employed in our approach and thus introduced as follows [18]....
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...For simplicity, we choose the definition as given in [18]....
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