Several methods can be used to perform distributed op- timization, either in a sequential or in a parallel manner, such as Lagrangian relaxation [21], augmented Lagrangian [15], approximate Newton directions in conjunction with stan- dard Lagrangian [16], [22] as well as the auxiliary problem principle [23]. These methods are however computationally cumbersome [24], [25] as they share the same synchronization that ties the different areas and demand strong coordination (each area optimizes its variables in every iteration and com- municates with its adjacent areas before moving to another iteration). The synchronous burden tends to cause degradation in performance mainly because of the inherent communication overhead and the idle processing time [26]. Among those methods, the technique known as the Alternating Direction Method of Multipliers (ADMM), while sharing the same per- formance limitations, has the advantage of converging faster than the aforementioned methods [27], [28], of being easier to implement, and of requiring less time and computational capacity at each processor. The structure of the iterations in this method makes their distribution among the existing processors easier than the previously mentioned methods [28]. Recently [29] proposed a fully asynchronous distributed version of the ADMM that is applied sequentially by randomly selecting overlapping areas of the network, the union of which covers the whole network. Despite the asynchrony, by relying on a careful analysis of the proximal splitting method [27] of which the ADMM is a special instance, it is proved that such an algorithm converges. As opposed to [29], which was not designed for DC-OPF problems specifically, in the present article, we additionally consider that the problem under study (being DC-OPF compliant) is such that the optimization variables are spread across the network (instead of being shared among the nodes) and that these variables have to satisfy some additional box constraints. In **power** **grid** terms, the **power** generated in the network are local quantities only

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Figure 4: AUC time series graph.
3.3 Step 3: Evaluation of Reliability Improve-
ment of the **Power** **Grid**
After the machine learning and data mining system out- puts, the feeders ranked with highest susceptibility to failure are usually treated with a higher priority. The final stage of the evaluation is to validate that the recommended actions are in fact leading to the expected **power** system improve- ment, i.e., fewer outages and longer time between failures. When considering longer time periods, a log(cumulative out- ages) versus log(time) chart is useful for seeing changes in the time interval between failures. This graphical analysis is also called a Duane plot, which is a log-log plot of the cu- mulative number of failures versus time [7], shown in Figure 5. The changing slopes of the regression lines show the im- proved rate of outages. If the failure rate had not changed, this log-log plot would show a straight line.

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The purpose of this paper is thus to analyze how the parameters of a regulatory review (duration, cost, and probability of success) affect the decision to invest in a simple model of investment under uncertainty. We consider a firm that contemplates making a lagged, irreversible investment, whose value varies stochastically. The firm must incur an upfront cash outlay to start the regulatory process, whose outcome is uncertain. Once regulatory approval has been granted, we consider two possible cases: 1) it is valid forever; or 2) it expires. The firm thus faces a sequential investment problem, where an initial investment is required to get the option of investing. To ground our numerical results, we apply our model to Hydro-Québec’s recent project proposal to add a 1250 MW (megawatts) interconnection to the Ontario **power** **grid**. 1

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One of the main reasons for concern about the reliability of the **power** **grid** is the age and state of the electrical infrastructure in many cities. According to the US Department of Energy’s **Grid** 2030 report (DOE 2003), “America’s electric system, ‘the supreme engineer- ing achievement of the 20th century,’ is aging, inefficient, and congested, and incapable of meeting the future energy needs of the Information Economy without operational changes and substantial capital investment over the next several decades.” Some parts of the energy **grid** are surprisingly old; in fact, some parts of the original electrical **grid** dating from 1880’s in the time of Thomas Edison are still in operation in New York, and probably the same is true of many other older US cities. According to a 2007 survey on reliability issues from the North American Electrical Reliability Corporation (NERC 2007), of all the issues considered to affect reliability, “Aging Infrastructure and Limited New Construction” was ranked first among all technical issues, with the highest likelihood and highest impact. In Manhattan alone, we calculated that at least 5% of the low-voltage distribution cables were installed prior to 1930, and many of these old cables are still functioning reliably. However, we are currently taking our electrical grids to the limit (or beyond the limit) of what they can handle, and emergency situations are occurring more and more often.

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not possible with the application of the RTS-96 single area **grid** due to the limited data provided for each component.
This paper’s purpose is to present the MIT risk ranking methodology as it applies to the bulk **power** **grid**. The load flow simulation model and the analysis of the RTS-96 test system used in the presentation of this methodology is not the focal point. Analysts of a real **power** **grid** are not bound to perform the infrastructure analysis in the manner described here and may choose any method of analysis suitable to meet their needs. The assumptions made in this paper are sometimes broad and may appear to oversimplify the analysis. By incorporating a more comprehensive assessment of the disutility of various failure scenarios, we do believe that the methodology presented here has advantages over the traditional contingency analysis performed today by many utilities and could

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Chapter 2
Architecture of the **power** **grid**
An electrical **grid**, or **power** **grid**, is an interconnected network for delivering electricity from producers to consumers. It consists of generating stations that produce electrical **power**, high voltage transmission lines that carry **power** from distant sources to demand centers, and distribution lines that connect individual customers. A scheme of a typical electric **power** **grid** is illustrated in Figure 2.1. Extrahigh-voltage electricity (380 kV and 220 kV) reaches the transmission **grid** from **power** plants as well as imports from abroad. The voltage must be as high as possible so that as much energy as possible can be transported over great distances with minimal losses. Depending on the target customer (industrial center or a typical family house) the voltage level is stepped down across multiple stages and different **grid** levels into medium- and low-voltage distribution grids. Recent developments in modern **power** grids involve widespread deployment of intermittent renewable generation, embrace installation of a wide variety of energy storage devices, as well as an increasing and widespread usage of electric vehicles. On the other hand, conventional energy sources are continually dis- continued, such as coal or nuclear **power** Swiss Federal Office of Energy [2018]. These developments motivate fundamental changes in methods and tools for the optimal daily operation and planning of modern **power** grids. Operational deci- sions taken by **power** system operators on a daily basis are commonly assisted by repeatedly solving complex optimization problems, aiming to determine optimal operating levels for electric **power** plants, so that the overall electricity genera- tion cost is minimized, while at the same time it satisfies load demands imposed throughout the transmission **grid** and meets safe operating limits. However, ex- ploitation of renewable energy sources and their **grid** integration poses many new challenges for **grid** operations due to their intermittent nature and high variabil- ity. New strategies for the operation and management of the electricity **grid** have

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1 PRESENTATION AND ISSUE
We present the results of the prediction of global radiation using Artificial Neural Networks (ANN) which are a popular artificial intelligence technique in the forecasting domain [1]. Inspired by biological neural networks, researchers in a number of scientific disciplines are designing ANNs to solve a variety of problems in decision making, optimization, control and obviously prediction [2-3]. In this context, our aim was to answer to the following question: Can we design an ANN of a site for which there is a lot of solar radiation data available and use this ANN to predict a PV **power** **grid** performance of another site? We tried to answer to this question with sites located on the island of Corsica (France). The island is characterized by a Mediterranean climate and a hilly terrain. The official meteorological network (from the French Meteorological Organization) is very poor: only three sites being about 50 km apart are equipped with pyranometers and enable measurements by hourly and daily step. These sites are Ajaccio (41°55‟N and 8°48‟E, seaside), Bastia (42°33‟N, 9°29‟E, seaside) and Corte (42°30‟N, 9°15‟E average altitude of 486 meters). In this study, we focus on the prediction of global solar irradiation on a horizontal plane for daily and hourly horizon. These time steps have been chosen according to the electricity supplier (EDF: Electricité De France) who is interested in the estimation of the fossil

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Infrastructure, e.g., public transportation, medical care and a vast number of other everyday life applications, rely on electrical **power** supply. Given the fact that modern **power** transmission grids, notably if they include renewable energy sources, differ significantly from conventional **power** grids with regards to topology and local dynamics [ 8 – 10 ], it is necessary to identify, understand, and cure the arising chal- lenges and problems. In particular, malfunctioning grids can be the result of **power** outages, which occur for various rea- sons, including line overload or voltage collapse. Here we will focus on the loss of synchrony. In normal operation, a **power** **grid** runs in the synchronous state in which all frequencies equal the nominal frequency (50 or 60 Hz) and in which steady **power** flows balance supply and demand at all nodes. When parts of a **power** **grid** desynchronize, destructive **power** oscillations emerge. To avoid damage, affected components must then be switched off. However, such switchings can in

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The contribution of chillers to the grid FR requirements is minimal in colder climates, where chiller power use is lower relative to other demand and each unit of installe[r]

Eco-Industrial Parks (EIP) aim to preserve environment while increasing competitiveness of companies. This paper presents a mathematical Mixed Integer Linear
Programming (MILP) model to optimally grassroots design an EIP energy network comprising heat and electricity. In the utility system, heated steam is produced, network is designed by selecting boilers and turbines technologies and interconnection pipes between companies. Simultaneously in the on-**grid** Hybrid **Power** System (HPS) composed of wind turbines, solar Photovoltaic (PV) panels, steam turbines and external **grid**, the model can select which source to use to meet the **power** demand. A case study of 10 industries from Yeosu real industrial park with seasonal data is provided to assess the model, first on economic comparison between stand-alone and EIP situation of companies, and secondly to determine which **power** source is profitable for HPS based on the sale price of electricity on the external **power** **grid**. In conclusion, this model allows the optimal design of the energy network of an EIP with dynamic data and with the objective of minimizing the net present cost.

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Understanding the multiscale properties of **power** grids
Multiple research results have shown that built-up space is often structured according to fractal logic and recent investigations have compared the coherency between the spatial organization of urban built-up spaces and street networks [10]. A similar approach is suitable for **power** systems. A given built-up area corresponds to an optimal topology of the **power** **grid**. This results from the spatial distribution of **power** sources and loads, the technical constraints, such as the maximal voltage variations, and the global cost. This latter cost is the sum of three components: the investment cost, the **power** loss cost and the non-supplied energy cost if the network is not reliable enough. Of course, the optimal solution is highly dependent on the spatial arrangement of the built-up area. Multiscale analysis aims to characterize this dependency at different scales of observation and determine how it influences the optimization of the **power** **grid** topology. For this purpose, the fractal dimensions of built-up areas are computed. These dimensions characterize how the built-up areas fill the space. Moreover, fractal analysis identifies scales in which spatial organization changes. To identify ruptures or shifts in the scaling behavior, a special method has been developed for urban pattern analysis [10]. A similar analysis can be performed for electrical distribution networks. This analysis can improve our understanding of the spatial organization of the distribution network on inter-urban and intra-urban scales and identify hypertrophies or deficiencies in existing networks. For instance, it intends to study the link between spatial distribution of consumers or decentralized energy sources in urban areas and network morphology.

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analyzed some of the weaknesses of the **power** **grid** such as the interconnection with Chinese and Laos **power** systems, the **power** swing protection (especially at Hatinh – Danang 500 kV transmission line in the central part of Vietnam), or over-voltages occurring when tripping heavily loaded lines. HVDC technologies could be a solution to those features. It was shown by simulation that, due to the capability of fast and independent active and reactive **power** control, VSC HVDC can greatly improve the stability of a **power** network. According to Lerch et al [31], strengthening the **power** transmission system by a separate 500 kV transmission system or HVDC connection between North and South can avoid the system separation at single faults. An alternative is to distribute more **power** generation across the country. In a report from World Bank technically realized by CESI it was considered that developing a long 500 kV HVDC line (700- 800 km) would constitute a viable solution and a pillar for the Smart **Grid** initiative in the **power** network of Vietnam [32].

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Experimentation location
The demonstrator is set up in the city of Carros, in the urban area of Nice, in the far South-East of France. Compared to the global French **power** system, this regional area is known as an electric peninsula, connected to the bulk **power** **grid** through a transmission corridor. In the district departments of Var and Alpes-Maritimes, the local generation represents only just ten percent of the consumption load. The area can hence be vulnerable, under load peaking conditions, to the risk of single contingency conditions or (N-1), on the transmission system. On summer, because of the Mediterranean weather conditions, the risk of forest fires is important also, so that events of disconnection of the aerial high-voltage lines may occur as well. Till 2010, one unique 400 kV line and one 225 kV line ensured the transmission of the energy from the neighbouring areas. Since then, the TSO has initiated network reinforcement programs in order to constitute a “safety net” with notably three additional 225 kV underground transmission lines [3]. In the future, replications of the advanced smart **grid** solutions such as developed within the Nice **Grid** project could also contribute to the strengthening of the reliability of the transmission flows.

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Eco-Industrial Parks (EIP) aim to preserve environment while increasing competitiveness of companies. This paper presents a mathematical Mixed Integer Linear
Programming (MILP) model to optimally grassroots design an EIP energy network comprising heat and electricity. In the utility system, heated steam is produced, network is designed by selecting boilers and turbines technologies and interconnection pipes between companies. Simultaneously in the on-**grid** Hybrid **Power** System (HPS) composed of wind turbines, solar Photovoltaic (PV) panels, steam turbines and external **grid**, the model can select which source to use to meet the **power** demand. A case study of 10 industries from Yeosu real industrial park with seasonal data is provided to assess the model, first on economic comparison between stand-alone and EIP situation of companies, and secondly to determine which **power** source is profitable for HPS based on the sale price of electricity on the external **power** **grid**. In conclusion, this model allows the optimal design of the energy network of an EIP with dynamic data and with the objective of minimizing the net present cost.

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duc to thcir bc-.:;.t pricc capacity ratio to makc profitable s1oragc use.
The main mathematic:al constraints are energy balances at **power** source which is supplied dircctly to the 1>0wcr demand or charged into storage. This cons1r . aint is availablc for each powc1· source and for cach type of clec1rical currem. Co11cerniog the dcmands. the 1>owcr demand must be satislied by cqui\ 1 alent **power** of sources or

E ov 86 kWh 38 kWh
Figure 7a clearly shows the advantages of the on-line control strategy which reduces the overshoot impacts compared to the use of the references issued from the off-line **power** dispatching. We can see from Table 4 that all performance criteria are significantly improved. It should also be noted that the largest overshoots occur in the afternoon (at around 3 p.m.) when the storage is fully charged by the important PV production. In practical, those overshoots could be avoided by derating PV production through MPPT control of PV arrays. Fig. 7b and Fig. 7c particularly illustrate the adaptation of the storage **power** flows for ensuring the **grid** **power** requirements in relation to forecast errors. This leads to some deviations on the storage **power** P st * and the

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VI. C ONCLUSION
Swells have non-negligible influences on the MCT generation system. Speed-based MPPT algorithm could cause severe generator **power** fluctuations in case of swell disturbance. In this paper, the swell effect is modeled based on the sea state and the MCT location parameters. The carried-out simulations show that the tip-speed ratio MPPT may cause severe **power** fluctuations in the generator **power**. A modified MPPT with filter strategy has been proposed utilizing the system inertia to reduce the generator **power** fluctuation as the first step of **power** smoothing control. The effectiveness of the proposed MPPT strategy is confirmed by comparing it to the tip-speed ratio MPPT and the torque- based MPPT. Simulation results have shown that the proposed MPPT and the torque-based MPPT lead to similar **power** fluctuation-reduction performance. The achieved results have shown the ability of the proposed MPPT to greatly reduce the generator **power** fluctuations with the optimized filter. It should also be mentioned that, for some MCTs with much flatter C p curves, the **power** fluctuation can be less severe than that dealt with in this study. The second step of **power** smoothing control is by integrating supercapacitors as the energy storage system to compensate the remaining generator **power** fluctuations. The sizing of the SC is calculated by energy requirement and voltage settings. The duty ratio of the SC is controlled through the charge and discharge requirements to achieve a smoothed **grid** target **power**. Simulation results have shown the effectiveness of the joint operation of the proposed MPPT and the SC.

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simulates a **grid** supporting a variety of dierent servi
es. Figures 2(a) and 2(b),
and Table 1 show the nodes' CPU utilization and the domain lo
ation over
time. First, we observe that the IVS strategy has CPU average load that is
almost equal for all four nodes (approximately 60%), whereas our solution tends

There are n 2 shortcuts in the **grid** (assuming q = 1);
When one wants to a shortcut, any of the n 2 − 1 other nodes can be chosen with non-null probability. This can be made by inverse transform sampling, with a cost Ω(n 2 ); The shortcut distribution depends on the node u considered, even if one uses relative coordinates. For example, a corner node will have i + 1 neighbors at distance i for 1 ≤ i < n, against 4i neighbors for inner nodes (as long as the ball of radius i stays inside the **grid**). This means that, up to symmetry, each node has a unique shortcut distribution 1 . This prevents from mutualising shortcuts drawings between nodes. In the end, building shortcuts as described above for each of the R runs has a time complexity Ω(Rn 4 ), which is unacceptable if one wants to evaluate e

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routing strategy manages to reach any destination after a few hops. This seminal work has inspired multiple studies from both the theoretical and empirical social systems communities.
In [4, 5], Kleinberg considers a directed random graph G(n, r, p, q), where n, p, and q are positive integers and r is a non-negative real number. A graph instance is built from a square lattice of n × n nodes endowed with the Manhattan distance d: if u and v are two nodes with respective coordinates (i, j) and (k, `), the distance between u and v is d(u, v) = |i − k| + |j − `|. The Manhattan distance represents some natural proximity (geographic, social, . . . ) between the nodes. Each node has local neighbors as well as long range neighbors. The local neighbors of a node u are the nodes v such that d(u, v) ≤ p. The long range neighbors of u, also called its shortcuts, are q nodes sampled independently and identically from a **power** law distribution: the probability that a given long range edge starting from u arrives in v is proportional to (d(u, v)) −r .

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