The Geometry of Power Systems Steady-State Equations– Part I: Power Surface

Steady-state equations play a fundamental role in the theory of power systems and computation practice. These equations are directly or mediately used almost in all areas of the power system state theory, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I considers steady states of the power system as a surface in the power space. A power flow feasibility region is shown to be widely used in power system theories. This region is a projection of this surface along the axis of a slack bus active power onto a subspace of other buses power. The findings have revealed that the obtained power flow feasibility regions, as well as marginal states of the power system, depend on a slack bus location. Part II is devoted to an analytical study of the power surface of power system steady states.

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

Economic Analysis of Trigeneration Systems Considering Participations of Energy Storage

Distributed trigeneration has been regarded as one of the leading solutions for the future energy production. Unlike centralized energy systems, trigeneration typically recovers otherwise wasted energy and supplies combined cooling, heating, and power products to end users simultaneously, which however causes difficulties in meeting weak temporal-correlated energy demands of end users. Inspired by the success in electric energy systems, energy storage may provide effective solutions to the challenges with respect to trigeneration by decoupling energy generation and consumption. However, multiple key questions are yet fully understood for planning storage-integrated trigeneration systems. The present study aims to answer the following questions: (i) what roles of energy storage are going to play in a trigeneration system? And (ii) how would energy storage affect the performance of the trigeneration system? A self-coded trigeneration system planning model is developed via Python programming to optimize capacities of different devices in the trigeneration system with the presence of energy storage to meet variable multi-energy demands. The effects of the energy storage on the performance of the trigeneration system are investigated. The underlying mechanisms of the energy storage affecting the system’s performance are also explored based on the feasibility region analysis and wasted energy analysis.

REDUCTION OF ACTIVE POWER LOSS & STATIC VOLTAGE STABILITY MARGIN ENHANCEMENT BY VIRAL SYSTEM ALGORITHM

This paper presents Viral Systems Algorithm (VSA) for solving optimal reactive power problem. VSA have proven to be very efficient when dealing with problems of high complexity. The virus infection expansion corresponds to the feasibility region exploration, and the optimum corresponds to the organism lowest fitness value. Many available algorithms usually present weaknesses and cannot guarantee the optimum output for the problem in a bounded time. Projected Viral Systems Algorithm (VSA) has been tested on standard IEEE 30 bus test system and simulation results show clearly about the superior performance of the proposed Viral Systems Algorithm (VSA) in reducing the real power loss and static voltage stability margin (SVSM) index has been enhanced.

Graph Space Embedding

We propose the Graph Space Embedding (GSE), a technique that maps the input into a space where interactions are implicitly encoded, with little computations required. We provide theoretical results on an optimal regime for the GSE, namely a feasibility region for its parameters, and demonstrate the experimental relevance of our findings. Next, we introduce a strategy to gain insight on which interactions are responsible for the certain predictions, paving the way for a far more transparent model. In an empirical evaluation on a real-world clinical cohort containing patients with suspected coronary artery disease, the GSE achieves far better performance than traditional algorithms.

Circuit Tolerance Design Using Belief Rule Base

A belief rule-based (BRB) system provides a generic nonlinear modeling and inference mechanism. It is capable of modeling complex causal relationships by utilizing both quantitative information and qualitative knowledge. In this paper, a BRB system is firstly developed to model the highly nonlinear relationship between circuit component parameters and the performance of the circuit by utilizing available knowledge from circuit simulations and circuit designers. By using rule inference in the BRB system and clustering analysis, the acceptability regions of the component parameters can be separated from the value domains of the component parameters. Using the established nonlinear relationship represented by the BRB system, an optimization method is then proposed to seek the optimal feasibility region in the acceptability regions so that the volume of the tolerance region of the component parameters can be maximized. The effectiveness of the proposed methodology is demonstrated through two typical numerical examples of the nonlinear performance functions with nonconvex and disconnected acceptability regions and high-dimensional input parameters and a real-world application in the parameter design of a track circuit for Chinese high-speed railway.

FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS

We consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

Credit Risk Evaluation Using a New Classification Model: L1-LS-SVM

Least squares support vector machine (LS-SVM) has an outstanding advantage of lower computational complexity than that of standard support vector machines. Its shortcomings are the loss of sparseness and robustness. Thus it usually results in slow testing speed and poor generalization performance. In this paper, a least squares support vector machine with L1 penalty (L1-LS-SVM) is proposed to deal with above shortcomings. A minimum of 1-norm based object function is chosen to get the sparse and robust solution based on the idea of basis pursuit (BP) in the whole feasibility region. Some UCI datasets are used to demonstrate the effectiveness of this model. The experimental results show that L1-LS-SVM can obtain a small number of support vectors and improve the generalization ability of LS-SVM.