Power Domination in Product Graphs

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graphs. We consider the graph theoretical representation of this problem as a variation of the dominating set problem and define a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph G is the power domination number $\gamma_P(G)$. We show that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs. On the other hand, we give a linear algorithm to solve the PDS for trees. In addition, we investigate theoretical properties of $\gamma_P(T)$ in trees T.

To monitor an electric power system by placing as few phase measurement units (PMUs) as possible is closely related to the famous vertex cover problem and domination problem in graph theory. A set P is a power dominating set (PDS) of a graph G = (V, E), if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number γp(G). In this paper, we determine the upper bounds of power domination number of generalized undirected de Bruijn graphs and generalized undirected Kautz graphs.

Due to the increasing penetration of gas-fired units and power to gas facilities, the electrical power system and natural gas system are more and more bi-directionally coupled. To tackle the challenges on the optimal scheduling operation of an integrated gas and power systems (IGPS), this article focuses on developing a novel approach to build a continuous spatial-temporal optimal operation schedule model. In the light of different time constants of the electrical power and natural gas systems, the continuous spatial-temporal optimal operation schedule model of IGPS is formulated in function space. Additionally, Bernstein polynomials are used to reformulate the continuous spatial-temporal optimization problem of IGPS to mixed-integer linear programming. In the study cases, the simulation results of a simple integrated system and a combined IEEE 39-bus power system and Belgian natural gas network demonstrate the accuracy and effectiveness of the proposed model.

Guest Editorial: Situational awareness of integrated energy systems

A set D of vertices of graph G is called a dominating set if every vertex is adjacent to some vertex . A set D to be a power dominating set of a graph if every vertex and every edge in the system are monitored by the set D. The power domination number γP (G) of a graph G is the minimum cardinality of a power dominating set of G. In this paper, we analyze the power domination number of corona graphs and join graphs. The corona product of two graphs G1 and G2 denoted by is defined as the graph G obtained by taking one copy of G1 and copies of G2, and then joined by an edge the i’th vertex of G1 to every vertex in the i’th copy of G2. The join of two graphs H1 and H2 is a graph formed from disjoint copies of H1 and H2 by connecting every vertex of H1 to every vertex of H2. Join graph H1 and H2 denoted by H1 + H2. The results show that the power domination number of some corona product and join graphs attain the lower bound.

Let $ G=G(V,E) $ be a graph. A set $ S\subseteq V $ is a power dominating set of $ G $ if $ S $ observes all the vertices in $ V,$ following two rules: domination and propagation. The cardinality of a minimum power dominating set is called the power domination number. In this paper, we compute the power domination number of generalized $ m $-Mycielskian of a cycle, $ C_n $. We found that it depends on the numbers $ n \an m $.

International Journal of Computational Engineering ScienceVol. 05, No. 01, pp. 81-89 (2004) No AccessEVOLUTIONARY PROGRAMMING BASED ECONOMIC DISPATCH WITH LINE FLOW CONSTRAINTSP. SOMASUNDARAM, K. KUPPUSAMY, and R. P. KUMUDINI DEVIP. SOMASUNDARAMSchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author , K. KUPPUSAMYSchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author , and R. P. KUMUDINI DEVISchool of Electrical and Electronics Engineering, Anna University, Chennai, Tamil Nadu 600 025, India Search for more papers by this author https://doi.org/10.1142/S1465876304002277Cited by:1 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThis paper presents an efficient, simple and new method for solving Economic Dispatch (ED) problem with line flow constraints through the application of Evolutionary Programming (EP). The controllable system quantities in the base-case state are optimized to minimize some defined objective function subject to the base-case operating constraints. A 10-bus system is taken for investigation. The ED results obtained using EP are compared with those obtained using quadratic programming. The investigations reveal that the proposed algorithm is relatively simple, reliable, efficient and suitable for on-line applications.Keywords:Power System OptimizationEconomic DispatchEvolutionary ProgrammingLine Flow Constraints References B. H. Chowdhury and S. Rahman, IEEE Transaction on power systems 5(4), 1248 (1990). Crossref, Google Scholar Nanda, L. Hari and M. L. Kothari, IEE Proceedings-C 141(1), 1 (1994). Google ScholarJ. Nandaet al., IEE Proceedings-C 139(1), 39 (1992). Google ScholarJ. Y. Fan and L. Zhang, IEEE Transactions on Power Systems 13(2), 320 (1998). Crossref, Google ScholarP. K. Hota, R. Chakrabarti and P. K. Chattopadhyay, Institute of Engineers (India) Journal-EL 81, 21 (2000). Google ScholarJ. Nanda and R. Badri Narayanan, Electrical Power and Energy Systems 24, 723 (2002). Crossref, Google Scholar D. B. Fogel , Evoluationary Computation: Toward a New Philosophy of Machine Intelligence ( IEEE Press , USA , 1995 ) . Google ScholarL. L. Lai and J. T. Ma, IEEE Transactions on Power Systems 12(1), 198 (1997). Crossref, Google ScholarH. T. Yang, P. C. Yang and C. L. Huang, IEEE Transactions on Power Systems 11(1), 112 (1996). Crossref, Google ScholarK. P. Wong and J. Yuryevich, IEEE Transactions on Power Systems 13(2), 301 (1998). Google ScholarT. Jayabarathi, G. Sadasivam and V. Ramachandran, Electric Power Systems Research 52, 261 (1999). Crossref, Google ScholarT. Jayabarathi and G. Sadasivam, European Transaction on Electrical Power 10(3), 167 (2000). Crossref, Google ScholarP. Attaviriyanupapet al., IEEE Transactions on Power Systems 17(2), 411 (2002). Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 1FDR PSO-based Transient Stability Constrained Optimal Power Flow Solution for Deregulated Power IndustryM. Anitha, S. Subramanian and R. Gnanadass28 Aug 2007 | Electric Power Components and Systems, Vol. 35, No. 11 Recommended Vol. 05, No. 01 Metrics History KeywordsPower System OptimizationEconomic DispatchEvolutionary ProgrammingLine Flow ConstraintsPDF download

Geodetic sets in graphs are briefly surveyed. After an overview of earlier results, we concentrate on recent studies of the geodetic number and related invariants in graphs. Geodetic sets in Cartesian products of graphs and in median graphs are considered in more detail. Algorithmic issues and relations with several other concepts, arising from various convex and interval structures in graphs, are also presented.KeywordsGeodetic numberGeodetic setCartesian productMedian graphBoundary set

A dominating set is a classic concept that is widely used in road safety, disaster rescue operations, and chemical graphs. In this paper, we introduce a variation of the dominating set: the proper 3-dominating set. For a proper 3-dominating set D of graph G, any vertex outside D is adjacent to at least three vertices inside D, and there exists one vertex outside D that is adjacent to three vertices inside D. For graph G, the proper 3-domination number is the minimum cardinality among all proper 3-dominating sets of G. We find that a graph with minimum degree at least 3 or one for which there exists a subgraph with some characteristic always contains a proper 3-dominating set. Further, we find that when certain conditions are met, some graph products, such as the joint product, strong product, lexicographic product, and corona product of two graphs, have a proper 3-dominating set. Moreover, we discover the bounds of the proper 3-domination number. For some special graphs, we get their proper 3-domination numbers.

An electric power system (EPS) with high-power-delivery and low-system-mass is required for wide body all electric aircraft (AEA). Cables are an essential component of this future EPS. At the cruising height of a wide-body aircraft the pressure is about 16.8 kPa. At that pressure, heat transfer to the ambient air by convection is strongly limited, so the distribution of temperature field across the aircraft cables is expected to be different from atmospheric pressure. The temperature field across the cable depends on the velocity field of the ambient air, which depends on the pressure and temperature. Also, to obtain the electric field of DC cables in the electric aircraft power system, the conductivity of the insulation, a function of temperature and electric field, should be calculated. In this paper, a 5 kV DC cable is studied at 16.8 kPa pressure to compare the cable's electric field and temperature field at low pressure to the atmospheric pressure. In our earlier research, we suggested novel EPS topologies for wide body AEA, and 5 kV DC is the voltage level that was taken into consideration. Moreover, the maximum permissible flowing current of the cable is investigated at the pressure of 16.8 kPa regarding the thermal limits of the cable. It is shown that at low pressures the temperature of the cable is highly increased compared to atmospheric pressure, so permissible current is lower than rated current.

As the cybersecurity situation continues to get tougher, more and more attackers are beginning to place their attention on power system networks, and the struggle between various countries is shifting from the real world to cyberspace. Power system network security protection is crucial. Humans have become inseparable from electricity, so it is vital to ensure power security. Whether for political or war purposes, many attacks related to power systems have occurred throughout history, resulting in extremely serious consequences and extremely high property damage. And power systems require special protection due to their high speed, high energy, and high-risk characteristics. In this paper, we analyze past network attacks on electric power systems, summarize common network attacks, analyze common network security protection means in the industry, dig into the progress of network security protection research on the electric power system, explore how traditional network security protection means including firewall, antivirus software, intrusion detection, and honeypot technology are applied on the electric power system.

For the research on crucial technologies of range-extended electric vehicle, the first problem to be solved is parameter matching and efficiency optimization for range-extended electric vehicle power and transmission system. Parameter matching and optimization of range-extended electric vehicle power and transmission system are multi-objective optimization problem. Evaluation and analysis of multi-objective optimization problem should be mutually independent and balanced. With the aim of guaranteeing vehicle’s comprehensive performance, a parameter matching and optimization method for range-extended electric vehicle power and transmission system is proposed in this paper. First, the house of quality model of range-extended electric vehicle is established to determine weight coefficient of vehicle performance indicator based on market requirements instead of experience. Based on co-simulation control model which is established in Matlab-Simulink and AVL-Cruise, 40 groups of orthogonal tests are performed, and the sensitivity of characteristic parameters is analyzed to explore the coupling law among vehicle performance indicators, so as to clarify the entry point for parameter matching and optimization. The simulation results show that the characteristic parameters not only have a significant influence but also have a coupling effect on the vehicle performance indicators. The analysis of variance shows that there is a limitation in optimal level combination of various factors only by range. Then, particle swarm optimization algorithm is selected to optimize the parameters of range-extended electric vehicle power and transmission system based on sensitivity analysis results obtained above. The study reveals that it is more efficient and reasonable to match the range-extended electric vehicle power and transmission system with a smaller battery capacity and a “medium-sized” auxiliary power unit which can achieve adequate dynamic performance, lower purchase cost, longer driving range and less energy consumption. Finally, a comparative simulation between the range-based analysis and particle swarm optimization-based analysis is conducted, the simulation results indicate that the optimized design parameters solution can significantly improve the technical indicators of the vehicle.

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.

The complexity of Dominating Set in geometric intersection graphs

Recently, there has been a focus on natural and man-made disasters with a high-impact low-frequency (HILF) property in electric power systems. A power system must be built with “resilience” or the ability to withstand, adapt and recover from disasters. The resilience metrics (RMs) are tools to measure the resilience level of a power system, normally employed for resilience cost–benefit in planning and operation. While numerous RMs have been presented in the power system literature; there is still a lack of comprehensive framework regarding the different types of the RMs in the electric power system, and existing frameworks have essential shortcomings. In this paper, after an extensive overview of the literature, a conceptual framework is suggested to identify the key variables, factors and ideas of RMs in power systems and define their relationships. The proposed framework is compared with the existing ones, and existing power system RMs are also allocated to the framework’s groups to validate the inclusivity and usefulness of the proposed framework, as a tool for academic and industrial researchers to choose the most appropriate RM in different power system problems and pinpoint the potential need for the future metrics.