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.

For highly populated Asian countries like Pakistan, the smart cities may play numerous positive roles resulting in efficient utilization of available infrastructure. This can be achieved by transforming existing infrastructures into smart ones. To start with such transformation, the main emphasis would be given to energy. For this purpose, the model of a framework capable of analyzing emerging trends in upcoming power system to make it more reliable. This research work focused on the significance of implementing advanced systems like smart grids. Therefore the proposed framework addresses the provision of an integrated simulation tool for in-depth study of system to determine susceptibility of failure, critical situations and restoration scheme by adding renewable energy resources. The planned framework will be used to analyze the impact of emerging trends in power grid operation of intelligent grid which is more commonly known as the smart grid. The framework may also be used to develop contingency plans to optimize the generation, transmission and distribution schemes thus providing the more flexible solutions. The proposed framework may also be used to enhance the security features of supervisory control and data acquisition system which is essential part of such smart transformations.

The paper presents a mathematical model of a power system (PS) consisting of a generating unit (with a synchronous generator) connected by a high voltage (transmission) power line to a bus. The state and output equations of the generator are expressed in the coordinate system d, q, 0 and with the use of phase quantities of the generator stator, the bus and the power line, which is especially useful in the analysis of asymmetrical states. A disturbance of the steady state in the form of a two-phase short-circuit in the transmission line was taken into account in the made calculations. The influence of the excitation system and angular speed control system of the generator as well as the impact of selected generator model parameters on the waveforms were investigated.

We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases.

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 decision-making process plays an important role in the development of society in general and the effective management of organizations in particular. In today's world, where the complexity of tasks and the competitive environment are constantly growing, making the right and informed decisions becomes a key element of success. Any person, group of people or organization is constantly faced with the need to choose between several possible courses of action, called alternatives, whether in the personal sphere or in the work of organizations. To effectively make complex decisions within the activities of organizations, models for making optimal decisions have been developed. The most popular of them is the model of decision-making under conditions of certainty, when the outcome of the decision is not influenced by random factors. All this confirms the relevance of scientific research in the field of decision making. Aim. The purpose of the study is to develop a methodology for assessing the degree of attractiveness of alternatives based on objective quantitative or subjective qualitative criteria, which will improve the quality of decisions made. The methodology is based on mathematical models for processing information containing the characteristics of alternatives according to evaluation criteria. Materials and methods. The methodology for evaluating alternatives presented in the work is based on mathematical models of information processing, which are based on methods of mathematical modeling, optimization methods, linear programming, theory of fuzzy sets, theory of latent variables, as well as methods of decision-making under conditions of uncertainty and methods of expert assessment. Results. The relevance of the development of a model for evalua¬ting construction projects according to quantitative criteria is shown, ways of solving the tasks are given and justified. A mathematical model has been developed that makes it possible to evaluate construction projects by objective indicators based on the theory of fuzzy sets and the Rush model for estimating latent variables. On the basis of numerical methods, the adequacy of the received estimates of construction projects is substantiated, the methodology for implementing computational procedures necessary for the practical implementation of evaluation models is described. Conclusion. The application of the given methodology in the decision-making procedure under conditions of certainty will improve the quality of decisions made and reduce the risks of their implementation.

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values

Activity-based models (ABMs) that simulate travel are becoming commonplace because of their value in supporting analysis of policy-driven scenarios. Because of the complex nature of ABMs, only a limited number of data sources provide the detail necessary for the estimation and calibration of these models. Of those sources, household travel surveys are becoming increasingly central to the development and calibration of ABMs. These models mimic rational decision making and use a hierarchical decision-making framework that prioritizes mandatory travel and activities, resulting in constrained time for other, nonmandatory activities. Therefore, it is critical that expanded household surveys represent mandatory travel and activity characteristics accurately. Traditionally, household surveys have been expanded to match household-level demographics, such as household size and number of vehicles. More recent weighting frameworks have included person-level demographics, such as worker status and age. However, there is limited research, if any, looking into the role of employment-level attributes (e.g., journey-to-work flow data) within the weighting procedure. This research built on the body of work in the areas of survey expansion and synthetic population generation to incorporate two employment-level variables, industry-level employment totals and home-to-work flow patterns, in the expansion process. Further, the employment-level variables were matched at different spatial resolutions: ( a) industry-level employment totals were matched at the regionwide level, and ( b) home-to-work patterns were matched at the subregional level to improve travel duration distributions. The resulting weights were then contrasted with results from traditional expansion methods by summarizing a variety of variables that are suitable for model validation.

The fuzzy set theory is being applied massively in many fields these days. One of these is linear programming problems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzy linear programming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheirfam and Hasani. In this paper, those cases are considered and numerical examples are solved.

Vendor Selection (VS) problem is considered as a critical decision that effects on the financial position for any firms. Hence the purchasing managers consider the selection process of the right vendors is a major function of the outsourcing process. Cost, quality, and services are three common criteria for VS problem. In the real cases the parameters of any problems are usually vague or not completely known, so that the Fuzzy Set Theory (FST) is one of the most powerful existing tools capable of addressing ambiguity and blurring information in parameters. A fuzzy parameters for VS problem are dealt with Linear Membership Function (LMF) through using cut that convert a fuzzy numbers to Interval Multiple Objective Linear Programming (IMOLP). The formulation of IMOLP is determined based on the value of , then IMOLP model is divided to upper and lower sub-models. A compromise interval solution will obtain from solving the sub-models as conventionally linear programming. The proposed approach is clarified with an illustrative example.

In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems; hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

Reliability of network operation is becoming an important issue due to increase in renewable energy sources (RESs). The system controllability is degenerating, while uncertainty due to RESs is increasing and threatening the system security. We refer to the robustness of power system in this context as “Robust Power System Security.” This paper proposes a new approach to monitor the region of robust power system security taking into account the conventional N-1 security criterion against uncertainties. Forecasted RESs and demands with their confidence intervals (CIs) are specified to formulate a problem for the evaluation of the size of the worst case feasible region, where positive size implies feasibility, while negative, infeasibility. A load dispatch problem using CIs of RESs forecast is studied to evaluate the region of robust power system security. The problem is formulated as bi-level optimization, which is linearized and transformed into the mixed integer linear programming (MILP) problem. This is a new approach in the treatment of uncertainties. Simulation results show that the proposed method is a promising approach to assess the degree of feasibility of system operation and planning.

In this paper, steelmaking-continuous casting (SCC) scheduling problem is investigated and a mixed integer linear programming model is developed. Since the technical constraints in the mathematical model are not defined exactly, fuzzy sets are used to present them. With using fuzzy constraints, a compromise between different criteria is made based on expert’s ideas in steel industry. Since the mathematical model is suitable only for small size problems, a hybrid algorithm is developed to solve the SCC scheduling problem. The proposed algorithm is based on a combination of particle swarm optimization and fuzzy linear programming (FLP) methods. In this algorithm, the process of generating a solution consists of two phases. In the first phase, assigning and sequencing the charges on machines is done, while in the second phase, a FLP model is applied to determine start time of charges on assigned machines. To evaluate the proposed procedure, it is compared with an algorithm reported in the literature through solving different problems. Numerical results show that the proposed algorithm can obtain very good solutions for SCC scheduling problem. The results also reveal the higher efficiency of the proposed approach in decreasing waiting time of charges between processing.

The integration of traditional and heuristic techniques is considered for the reactive power/voltage control program. The steady-state reactive power problem is addressed. Fuzzy sets are used to modify the linear programming (LP) approach to voltage control and to incorporate some heuristic concepts of the expert system approach. Multiple objectives and soft constraints are modeled using fuzzy sets. Piecewise linear convex membership functions for the fuzzy sets are defined. Under this definition, the fuzzy optimization problem is reformulated as a standard linear programming problem. The objective function represents the compromise among the original competing objectives and the soft constraints. In addition, discrete constraints are considered. Numerical examples demonstrate the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>