Constructing Convex Inner Approximations of Steady-State Security Regions

With the enhanced interaction between the AC and DC power system, the post-contingency cascaded DC commutation failure (CF) has been a potential security risk. This paper proposes the steady-state security region (SSR) formulation with the post-contingency cascaded CF considered. The voltage reduction at the post-contingency quasi-steady-state is selected to identify the cascaded CF. The decoupled linearized power flow (DLPF) is introduced so that the voltage issues can make contributions to the SSR depiction. The proposed SSR provides the scope of the dispatch decisions where the cascaded CF can be inhibited. Case studies between different types of SSR are performed in the IEEE modified 9- and 30-bus test systems to validate the effectiveness of the proposed SSR.

This chapter presents the concept and definition of the security region, and introduces major methods used in steady-state security region analysis of power system operation: the security corridor, the traditional expansion method, the enhanced expansion method, linear programming, and the fuzzy set theory. The main idea of security regions is to obtain a set of security injections explicitly so that for security assessment one need only check whether a given injection vector lies within the security region. To enhance the calculation speed of the regions, the following measures: adoption of calculation step, constraints are divided into two groups based on the threshold value shown in the equation, are adopted in the new expanding method. The chapter presents a new approach to construct the steady-state security regions of power systems, that is, the maximal security regions are directly computed using the optimization method.

Steady-state security assessment in distribution systems with high penetration of distributed energy resources

An adaptive pattern recognition approach based on an artificial neural network for calculation of steady state security is outlined. A Rumelhart feedforward net with error back-propagation learning scheme is described and implemented on a CIGRE 225 kV, 10 bus 13 lines system. The steady state security index obtained for a test case shows the capability and adaptability of this network. By backward propagation it is possible to obtain the combination of inputs (features) which give rise to the particular class membership. This information can be of great use in determining the necessary preventive and emergency actions to be taken when the system is in an insecure state. Though the results are very encouraging further efforts are required to make it an efficient and viable tool for steady state security analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

With high-level variable renewable energy integrating into power systems, the uncertainty significant challenges to the real-time dispatch (RTD). Meanwhile, the influence of voltage magnitude and reactive power on RTD always were ignored. Based on effective steady-state security regions of power systems and linear power flow model, a real-time dispatching method considering voltage magnitude and reactive power is proposed in this paper. This model has two goals, one is the security goal, the other is the economic goal, and priority of security objectives is higher than economy. Unlike previous real-time dispatch methods, all of the operation base point, reactive power output and participation factors of automatic generation control (AGC) generators are chosen as decision variables in the model. In order to ensure computational efficiency, the model is finally transformed into a deterministic linear programming (LP) problem by robust optimization and other methods. The accuracy and computational efficiency of the method are illustrated by modified IEEE 9-bus system and IEEE 118-bus system.

The nonlinear evolution of a terrace edge during growth in the step-flow configuration is investigated. Starting from the constitutive growth equations of Burton, Cabrera, and Frank [Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)], we show that the dynamics of an isolated terrace edge, i.e., in the absence of any kind of step-step interaction, is described, close enough to the morphological instability threshold found by Bales and Zangwill [Phys. Rev. B 41, 5500 (1990)], by a nonlinear partial differential equation. This equation, although it emerges physically in a somewhat disguised manner, can be simply interpreted as representing the growth with an effective negative line tension, a stabilizing line diffusionlike process along the edge, and a quadratic nonlinearity restoring the Galilean invariance. This nonlinear equation, despite its apparent simplicity, manifests a variety of dynamics, ranging from simple steady-cellular structures to spatiotemporal chaos. When the system size is large enough, chaotic dynamics always prevails. We argue here that when the step-step interaction is important, however, one expects ``regular'' solutions, such as steady-cellular, broken-parity-traveling, and oscillatory modes, to be stable over a finite range of control parameters.

SUMMARY Recent spectral studies of vertical transect profiles of landscapes and mountains have shown them to be self-affine fractals, i.e. the rms height fluctuation Ah(L) averaged over a distance L scales as Ah(L) - Lx with x = 0.5 f 0.1, related to the fractal dimension Df = 2 - x = 1.5 of the horizontal contours. We propose that self-affine rough landscapes are created by the interplay of non-linearity and noise. To illustrate this idea and model the formation of such structures, we suggest a non-linear stochastic equation ahla? = DV*h + A(Vh)' + ~(r, t), which is the generalization of the deterministic Culling's linear equation. The non-linear term h(Vh)* comes from the requirement that erosion is proportional to the exposed area of the landscape; the noise term ~(r, t) accounts for the fact that erosion is locally irregular, as a result of the heterogeneity of soils and distribution of storms. Using this general framework, we recover the scaling law Ah(L) - Lx with x 2 0.4. Several novel avenues of research emerge from this analysis to further quantify geological data.

The performance of Particle Swarm Optimization (PSO) brings attention to the field of algorithms when deals with different optimization problems. Due to her simple implementation, small consumption, and very effective in finding a solution in many problems, (PSO) becomes well known to the field of algorithms. In addition, the late proposed algorithms mostly are compared to the well-known algorithm such as PSO. Thus, the Global African Buffalo Optimization (GABO) was proposed lately and yet not been compared to the old well-known algorithms in terms of accuracy and time consumption. However, in this paper, a comparison between Particle Swarm Optimization (PSO) and Global African Buffalo Optimization (GABO) algorithms was performed. Five different nonlinear equations with their upper and lower boundaries values were selected as the test optimization functions problem in addition to PSO was applied to real case study. The experimental results illustrated the differences in the performances of both algorithms toward the optimum solution. At the end of the experiments, the PSO algorithm quickly convergence towards the optimum solution using a few particles and iterations rather than GABO. However, the experimental result showed that PSO achieved good results in all the test cases within a short time. In many cases, PSO and GABO are promising optimization methods.

The process of regression testing is generally done under critical time and resource constraints. In the existing approaches, Test Case Prioritization (TCP), Test Case Selection (TCS), and Test Suite Reduction (TSR) have been treated as different optimization problems. This is based on simple heuristics that do not use valuable information that can be extracted from the program under test. Moreover, they do not allow for making internally consistent budget-conscious decisions. This paper introduces a unified approach that combines various variants of Graph Neural Networks (GNNs) and Reinforcement Learning (RL) for the solutions of TCP, TCS, and TSR. In our proposal, the representation of regression artifacts such as test cases, code entities, and faults is used as nodes in the typed graph, while the edges are used to show the relations between these artifacts. The relation-aware GNN is used for generating test case embeddings, reflecting the distance between the test cases and the changed areas as well as the areas known to have issues in the past. The actor-critic RL agent uses these test case embeddings and the budget to decide whether to run, skip, or discard test cases. The performance of our proposal outstrips coverage-based heuristics, history-based ranking, a GA-based search, an enhanced QPSO, and two learning-based ablations, as validated by our experiments on four Java projects from Defects4J. In terms of various programs and budgets, using GNN–RL has led to an improvement in the Average Percentage of Faults Detected (APFD) and Cost-cognizant Average Percentage of Faults Detected (APFDc) by approximately 6–9 percentage points on lower budgets. In addition, it is possible to obtain a 42% suite reduction and a 48% cost reduction while still retaining 98% of all fault-revealing tests in the final suite. The results show that it is possible to obtain promising solutions for adaptive regression testing using budget-aware reinforcement learning and graph-based representation learning.

Using conventional two-dimensional nonlinear shallow water equations and the associated semi-momentum finite difference schemes, the nonlinear interaction between storm surges and tides, caused by eight tropical cyclones of different tracks over the coastal waters of Shanghai is numerically studied in this paper. The contributions of various nonlinear terms in the dynamic equations to the water level heights is diagnostically analyzed in detail. It is shown that the nonlinear bottom friction term is of prime importance in controlling the water level and nonlinear tide-surge interaction. The correction to the water level and storm surge due to tide-surge interaction is significant.

Optimization Planning Method of Distributed Generation Based on Steady-State Security Region of Distribution Network

In this paper, we propose an iterative framework for solving the stochastic transmission capacity expansion planning (TCEP) optimization problem with N-1 contingency analysis. A three-level filtering algorithm is designed that uses developed important scenario identification index (ISII) and similar scenario elimination (SSE) technique to decrease the number of reliability constraints in stochastic TCEP in a systematic and trackable way. This filter decreases structural constraints in our TCEP mixed-integer programming formulation in each iteration (up to 99.8% in the first iteration), and the iterative framework adds reliability constraints into the optimization problem gradually in order to decrease the total simulation time. A lower bound is calculated to quantify the quality of results. To verify capabilities of the proposed method, it is applied to a reduced ERCOT system with 317 buses, 427 binary variables, and ten scenarios. The numerical result shows that the proposed method can solve large-scale stochastic TCEP optimization problems faster, and its relative performance improves with increasing number of scenarios and the system size.

Various software engineering paradigms and real-time projects have proved that software testing is the most critical and highly important phase in the SDLC. In general, software testing takes approximately 40–60% of the total effort and time involved in project development. Generating test cases is the most important process in software testing. There are many techniques involved in the automatic generation of these test cases which aim to find a smaller group of cases that could allow for an adequacy level to be achieved which will hence reduce the effort and cost involved in software testing. In the structural testing of a product, the auto-generation of test cases that are path focused in an efficient manner is a challenging process. These are often considered optimization problems and hence search-based methods such as genetic algorithm (GA) and swarm optimizations have been proposed to handle this issue. The significance of the study is to address the optimization problem of automatic test case generation in search-based software engineering. The proposed methodology aims to close the gap of genetic algorithms acquiring local minimum due to poor diversity. Here, dynamic adjustment of cross-over and mutation rate is achieved by calculating the individual measure of similarity and fitness and searching for the more global optimum. The proposed method is applied and experimented on a benchmark of five industrial projects. The results of the experiments have confirmed the efficiency of generating test cases that have optimum path coverage.

Global solutions and self-similar solutions for nonlinear beam equations

The present paper studies the blow-up of solutions to nonlinear wave equations whose nonlinear terms are proposed by F. John. We shall show that the solutions to the equations in two space dimensions blow up at finite time if the power in nonlinear term is equal to or smaller than three. Our basic idea is to use the fundamental identity for the iterated spherical means.