Network Theory Based Power Grid Criticality Assessment

Transmission utilities faces problems to feed loads during the peak load conditions due to the critical network constraints. The constraints are to be identified in advance and feasible solutions will help to maintain uninterrupted power supply during the peak load scenario. This paper presents a detailed study to identify the transmission constraints of the utility network in southern parts of Rajasthan, India to feed peak load demand of 550 MW approximately. Critical transmission lines are identified and also the ring open and close status of 132 kV transmission lines in the region is also identified to simulate real time network operating scenario. Possible solutions are identified by performing loads flow study for the two scenario of base case network and nine proposed scenarios. Proposed scenarios are realized by considering the possible solutions which helps to overcome the transmission constraint of unequal loadings on the critical transmission lines. This is concluded that transmission constraint may be mitigated either by changing network operating topology by diverting the loads or by construction of new transmission lines. Study is performed using the MiPower software simulating the practical transmission network in Southern Parts of Rajasthan.

Gerilim kararlılığı, güç sistemlerinde incelenmesi gereken önemli bir konudur. Sürekli artan elektrik enerjisi talebi, artan talebi karşılamak için yeni elektrik üretim santrallerinin kurulumu ve güç sistem arızaları gerilim kararlılığını olumsuz yönde etkilemektedir. Günümüzde gerilim kararlılığını iyileştirmek için güç sistemlerinde Esnek Alternatif Akım İletim Sistemleri (FACTS cihazları) kullanılmakta olup, ayrıca enerji talebini karşılamak ve gerilim kararlılığını iyileştirmek için güç sistemlerine Dağıtık Üretim Kaynakları (DGs) entegre edilmektedir. Bu çalışmada, IEEE 30 baralı güç sistemi ile Kuzeybatı Anadolu (KBA) güç sistemi, gerilim kararlılığı bakımından temel (nominal), aşırı yüklenme ve hat kopması durumlarında incelenmiştir. İncelenen güç sistemlerine FACTS cihazlarından Statik Var Kompanzatör (SVC) ve Tristör Kontrollü Seri Kapasitör (TCSC), DGs’lerden ise Yakıt Hücresi (YH), Güneş Enerji Santrali (GES) ve Rüzgâr Enerji Santrali (RES) ayrı ayrı ve birlikte bağlanmıştır. Güç sistemlerinin bara gerilim değerlerinde ve yüklenme parametresinde meydana gelen değişimler analiz edilmiştir.

SYNOPSES In the UK, the Electricity Act of 1989 was amended in 2000 to remove the distinction between private and public electric supply companies. The customers in the UK saved £ 700 million in one year under de-regulation. In the US, Congress passed the Energy Policy Act in 1992 that de-regulated the wholesale electric market and mandated electric utilities to open up the transmission system on an equal basis to all who utilize it. During the past decade, the demand for electricity in the United States has increased by 35 percent, whereas, the generation has increased only by 18 percent. With the bulk power transactions and reservations, the transmission system now operates closer to its stability limits. Voltage instability occurs when the balance between the reactive power producing sources and the VAR losses cannot be maintained. The limited construction of new transmission lines has pushed the power industry toward the development of advanced technologies such as flexible ac transmission system (FACTS), static VAR compensators (SVC), static synchronous compensators (STATCOM), unified power controllers (UPFC), and distributed superrconducting magnetic energy storage (D-SMES). In a nuclear power plant, offsite and onsite electric power systems are required to provide sufficient capacity and capability to assure that the containment integrity be maintained during power operation or in case of a postulated accident. Analyses must verify that the electric grid remains stable in case of loss of the nuclear unit, the largest other unit on the grid or the most critical transmission line and a change it due to deregulation would affect those analyses. Nuclear Regulatory Commission (NRC) staff ensures that the licensees maintain adequate voltages to the Class 1E (safety) buses. If the operator has failed to restore adequate voltages, the Class 1 E buses should be automatically separated from the offsite power system and connected to the emergency diesel generators. Most utilities use on-line contingency analysis and the control centers notify them when the offsite power system in their nuclear plant is degraded. The control centers use load conservation procedures to provide the plant a stable offsite power system. The control centers have assured the NRC staff that the nuclear power plants are their preferred customers and that they will be provided with an adequate offsite power system even under reduced grid generation availability. This paper discusses the voltage stability, power transfer limits, reactive reserves, methods of improving voltage stability (such as superconductivity), load conservation procedures and effects of deregulation on nuclear power generating stations.

This paper presents the influence of critical transmission line outage on the allocation of reactive power loss in a deregulated power market. An alternative approach of Transmission Line Coupling Matrix (TLCM) technique, which identifies the critical transmission lines whose outages could result in total blackout within the network, is revisited. The theoretical framework and mathematical formulations of the approach are presented. Based on the fundamental circuit laws, the topological structure of the network is captured in the system Y-bus matrix and used to determine the reactive power allocation to each network participant. The reactive power loss associated with each bus is then determined and also allocated to each network player. The influential transmission lines, whose failure could lead to network collapse, are identified using TLCM approach. The reactive power loss allocations in power systems, operating under normal condition as well as under critical contingency due to outage of influential transmission lines, are then investigated. The results obtained show the effectiveness of the approach.

Some critical lines can have important impact on the large-scale blackouts and cascading failures in power grid. Based on the newest progress in the field of complex network, a new vulnerability index called weighted line betweenness is proposed as vulnerability index in this paper. The weighted line betweenness of one line is defined as the sum of the loads acted on this line, which are brought by the shortest electric paths between generator nodes and load nodes that passing through this line. We revise the weighted line betweenness by increasing the betweenness to the highest betweenness in the neighboring lines before revision. Vulnerability analysis has been carried out on the IEEE 39 bus system and Huazhong-Chuanyu power grid. The time domain simulation results verify that the weighted line betweenness can not only identify the most critical lines but also find out those light loaded but critical lines due to their special position in the power grid.

Concern about electromagnetic field (EMF) effects on human health has heightened public awareness of overhead transmission lines planning and operation. The objective of this paper is to study the effect of EMF constraints on optimal power generation scheduling. This study considers reducing EMF levels associated with critical transmission lines by redistributing the scheduled power generation, while maintaining the minimum operation cost as an objective. The EMF constraints are given in terms of control variables and fuzzy sets are utilized to model the tradeoff between minimizing the objective function and satisfying EMF constraints. Numerical results for the application of the proposed approach to test systems are discussed. >

Cascading failures are the typical reasons of blackouts in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure a higher level of robustness of power grids. Metrics from Complex Networks are widely used to investigate the grid vulnerability. Yet, these purely topological metrics fail to capture the real behaviour of power grids. This paper proposes a metric, the effective graph resistance, as a vulnerability measure to determine the critical components in a power grid. Differently than the existing purely topological measures, the effective graph resistance accounts for the electrical properties of power grids such as power flow allocation according to Kirchoff laws. To demonstrate the applicability of the effective graph resistance, a quantitative vulnerability assessment of the IEEE 118 buses power system is performed. The simulation results verify the effectiveness of the effective graph resistance to identify the critical transmission lines in a power grid.

Maximum flow problem on dynamic generative network flows with time-varying bounds

Augmenting path algorithms, first introduced by Ford and Fulkerson (Ford, L. R., D. R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J.), are widely used in optimization. Examples include Schönsleben's polymatroid intersection algorithm (Schönsleben, P. 1980. Ganzzahlige polymatroid-intersection-algorithmen. Ph.D. thesis, Eidgenössischen Technischen Hochschule, Zürich.), the maximum polymatroidal network flow algorithm of Lawler and Martel (Lawler, E. L., C. U. Martel. 1982. Computing maximal polymatroidal network flows. Math. Oper. Res. 7 334–347.), Frank's algorithm for the Edmonds–Giles polyhedron (Frank, A. 1984. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory Ser. B 36 221-239.) and Cunningham's algorithm for testing membership in matroid polyhedra (Cunningham, H. W. 1984. Testing membership in matroid polyhedra. J. Combin. Theory Ser. B 36 161–188.). Here we give an order of magnitude improvement for the above algorithms by using an approach analogous to that of Dinits’ maximum flow algorithm (Dinits, E. A. 1970. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. 11 1277–1280.).

The problem of integer balancing of a four-dimensional matrix is studied. The elements of the inner part (all four indices are greater than zero) of the given real matrix are summed in each direction and each two- and three-dimensional section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements with the largest previous or the smallest following integer. At the same time, the element with four zero indices should be produced with standard rules of rounding - off. In the article the problem of finding the maximum multiple flow in the network of any natural multiplicity is also studied. There are arcs of three types: ordinary arcs, multiple arcs and multi-arcs. Each multiple and multi-arc is a union of linked arcs, which are adjusted with each other. The network constructing rules are described. The definitions of a divisible network and some associated subjects are stated. There are defined the basic principles for reducing the integer balancing problem of an -dimensional matrix ( ) to the problem of finding the maximum flow in a divisible multiple network of multiplicity . There are stated the rules for reducing the four-dimensional balancing problem to the maximum flow problem in the network of multiplicity 5. The algorithm of finding the maximum flow, which meets the solvability conditions for the integer balancing problem, is formulated for such a network.

We are currently witnessing a change of electrical power supply from conventional power generation to power generation based on renewable energy sources such as wind and solar power. The main differences between these two ways of power generation are that power generation based on renewables produces typically less and more fluctuating power output. The changes in power production therefore pose a problem for the stability of power grids. In this thesis we analyze different effects of these changes for the stability of power grids. In the first part we introduce in detail the power grid model we are using. We analyze the model for the simplest possible system, a system consisting of one generator and one consumer. For this system an analytical analysis of the model is possible. We demonstrate that the model contains the most important features of real-world power grids and is such a useful tool for investigations of larger networks. The most important feature is that there exists both a stable and an unstable state and the dynamics depend on the initial conditions, i.e., the current state of the network. In the second part of the thesis we investigate the process of decentralization of power generation. This process is ongoing due to the replacement of conventional power sources with renewables. As renewable power sources are typically far away from consumers the replacements process ends up with a decentralized power grid. Our main results are that dynamical stability, i.e., stability against large scale power perturbations, is decreased for decentralized power grids compared with centralized ones. On the other hand, structural stability, i.e., stability against single transmission line failures, is increased for decentralized grids. In the last part we analyze structural stability in more detail. We develop a novel criterion to predict which transmission lines can induce large scale power outages if they fail and which not. We demonstrate that the load of a transmission line alone is not a good predictor for this behavior.

We provide a comprehensive study on network flow problems with arc reversal capabilities. The problem is to identify the arcs to be reversed in order to achieve a maximum flow from source(s) to sink(s). The problem finds its applications in emergency transportation management, where the lanes of a road network could be reversed to enable flow in the opposite direction. We study several network flow problems with the arc reversal capability and discuss their complexity. More specifically, we discuss the polynomial time algorithms for the maximum dynamic flow problem with arc reversal capability having a single source and a single sink, and for the maximum (static) flow problem. The presented algorithms are based on graph transformations and reductions to polynomially solvable flow problems. In addition, we show that the quickest transshipment problem with arc reversal capability and the problem of minimizing the total cost resulting from arc switching costs are \(\mathcal{NP}\) -hard.

This paper investigates the application of a minimum loss path finding algorithm to determine the maximum flow in generalized networks that are characterized by arc losses or gains. In these generalized network flow problems, each arc has not only a defined capacity but also a loss or gain factor, which must be taken into consideration when calculating the maximum achievable flow. This extension of the traditional maximum flow problem requires a more comprehensive approach, where the maximum amount of flow is determined by accounting for additional factors such as costs, varying arc capacities, and the specific loss or gain associated with each arc. This paper extends the classic Ford–Fulkerson algorithm, adapting it to iteratively identify source-to-sink (s − t) residual directed paths with minimum cumulative loss and generalized augmenting paths (GAPs), thus enabling the efficient computation of maximum flow in such complex networks. Moreover, to enhance the computational performance of the proposed algorithm, we conducted extensive studies on parallelization techniques using graphics processing units (GPUs). Significant improvements in the algorithm’s efficiency and scalability were achieved. The results demonstrate the potential of GPU-accelerated computations in handling real-world applications where generalized network flows with arc losses and gains are prevalent, such as in telecommunications, transportation, or logistics networks.

Protection system communications are increasing in importance because they enable optimal operation of power systems. Because of the high cost of communications systems in the past, protection systems had to be optimized to use minimum bandwidth and were often forced to rely on a single bit of information. A synchronous 64 kbps channel reserved exclusively for the most critical transmission lines was seen as the best-case scenario. Communications system developments over the last three decades have opened a deluge of information, with a single optical fiber now capable of carrying multiple terabits of data simultaneously. Modern protection systems face a totally different problem. Communications bandwidth is almost unlimited, but the channel must be shared with other users and may present multiple challenges, such as channel asymmetry, variable latency, path reconfiguration due to automated failure recovery, packet-based transport, and the need for system-wide time synchronization. This paper reports on an experimental investigation that uses coarse or dense wavelength division multiplexing (CWDM, DWDM) for applications in high-speed traveling-wave protection. The investigation was performed using the latest generation of carrier-grade optical transport network (OTN) equipment. The paper documents the performance, opportunities, and pitfalls associated with this application and outlines practical strategies for the seamless integration of protection systems with the latest generation of OTN technologies.

Centrality measures based on network topology are valuable for decision-making in complex systems. These measures allow the identification of the most essential elements of the network, i.e. those that have the most significant impact on the overall operation of the system. In the case of electricity grids, centrality measurements can be used to identify the most crucial power plants, the most critical transmission lines, or the most vulnerable connection points. This information can be used to improve network planning and control to ensure a reliable and secure electricity supply. In this paper, centrality measures are used to identify those nodes in the Mexican electricity network that are topologically the most relevant. These are used to locate frequency meters that act as critical points for frequency control. Results are presented for an equivalent network of 190 busbars divided into geographical control regions.