This paper surveys the literature related to the evolution of cellular communications as a key enabling technology for fundamental operations of smart grid neighborhood area networks (NANs). The latest releases of the LTE standard, representing the recent advancements in cellular technology, offer significant benefits to the modernization of the aging power distribution grid compared with other communication technologies. However, since LTE was not originally designed for smart grid applications, important challenges remain unsolved before it can efficiently support advanced NAN functionalities. This survey identifies the limitations of LTE and provides a comprehensive review of the most relevant proposed architectural and protocol enhancements for the communication infrastructure associated with smart grid NANs that can be found in the literature to date. As device-to-device (D2D) communications in LTE standards are a promising technology for reducing delay and boost reliability, this paper dwells on the potential gains that can be achieved by enabling direct communication using cellular networks, and also discusses in detail LTE-D2D applicability in representative NAN use cases in the power distribution grid. We conclude by stating open issues and providing research directions for future research in the field. This paper constitutes the first comprehensive survey of proposed LTE-enhancement and D2D solutions for smart grid NANs.

Cellular Communications for Smart Grid Neighborhood Area Networks: A Survey

In this paper we use the planar circular restricted three-body problem where one of the primary bodies is an oblate spheroid or an emitter of radiation in order to determine the basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the values of the mass ratio $\mu $
 , the oblateness coefficient $A_{1}$
 , and the radiation pressure factor $q$
 vary in predefined intervals. The regions on the configuration $(x,y)$
 plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson method. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed in order to obtain the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation demonstrating how the dynamical quantities $\mu $
 , $A_{1}$
 , and $q$
 influence the basins of attractions. Our results suggest that the mass ratio and the radiation pressure factor are the most influential parameters, while on the other hand the structure of the basins of convergence are much less affected by the oblateness coefficient.

Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

We study numerically the photogravitational version of the problem of four bodies, where an infinitesimal particle is moving under the Newtonian gravitational attraction of three bodies which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle. The fourth body does not affect the motion of the three bodies (primaries). We consider that the primary body m
 1 is dominant and is a source of radiation while the other two small primaries m
 2 and m
 3 are equal. In this case (photogravitational) we examine the linear stability of the Lagrange triangle solution. The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves, as well as the positions of the equilibrium points on the orbital plane are given. The existence and the number of the collinear and the non-collinear equilibrium points of the problem depends on the mass parameters of the primaries and the radiation factor q
 1. Critical masses m
 3 and radiation q
 1 associated with the existence and the number of the equilibrium points are given. The stability of the relative equilibrium solutions in all cases are also studied. In the last section we investigate the existence and location of the out of orbital plane equilibrium points of the problem. We found that such critical points exist. These points lie in the (x,z) plane in symmetrical positions with respect to (x,y) plane. The stability of these points are also examined.

Equilibrium points in the photogravitational restricted four-body problem

In this paper, families of simple symmetric and non-symmetric periodic orbits in the restricted four-body problem are presented. Three bodies of masses m1, m2 and m3 (primaries) lie always at the apices of an equilateral triangle, while each moves in circle about the center of mass of the system fixed at the origin of the coordinate system. A massless fourth body is moving under the Newtonian gravitational attraction of the primaries. The fourth body does not affect the motion of the three bodies. We investigate the evolution of these families and we study their linear stability in three cases, i.e. when the three primary bodies are equal, when two primaries are equal and finally when we have three unequal masses. Series, with respect to the mass m3, of critical periodic orbits as well as horizontal and vertical-critical periodic orbits of each family and in any case of the mass parameters are also calculated.

Families of periodic orbits in the restricted four-body problem

In a traffic jam or dense vehicle environment, vehicular ad hoc networks (VANETs) cannot meet the safety requirement due to serious packet collisions. The traditional cellular network solves packet collisions but suffers from long end-to-end delay. Third-Generation Partnership Project (3GPP) Long-Term Evolution (LTE) overcomes both drawbacks; thus, it may be used, instead of VANETs, in some extreme environments. We use Markov models with dynamic scheduling and semipersistent scheduling (SPS) to evaluate how many idle resources of LTE can be provided for safety services and how safety applications impact LTE traditional users. Based on the analysis, we propose to reserve the idle radio resources in LTE for vehicular safety services (LTE-V). Additionally, we propose the weighted-fair-queuing (WFQ) algorithm to schedule beacons for safety services using the LTE reserved resources. Numerical results verify that the proposed mechanism can significantly improve the reliability of safety applications by borrowing limited LTE bandwidth. We also build an NS3 simulation platform to verify the effectiveness of the proposed Markov models. Finally, the reliability of applications, including cooperation collision warning (CCW), slow vehicle indication (SVI), and rear-end collision warning (RCW), using dedicated short-range communication (DSRC) with LTE-V, are evaluated. The simulation results demonstrate that the stringent quality-of-service (QoS) requirement of the aforementioned three applications can be satisfied, even under heavy traffic.

Analytical Model and Performance Evaluation of Long-Term Evolution for Vehicle Safety Services

We study numerically the problem of four bodies, three of which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle, while the fourth is infinitesimal. The fourth body does not affect the motion of the three bodies (primaries). The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves as well as the positions of the equilibrium points are given. The existence and the number of collinear and noncollinear equilibrium points of the problem depend on the mass parameters of the primaries. For three unequal masses, collinear equilibrium solutions do not exist. Critical masses associated with the existence and the number of equilibrium points, are given. The stability of the relative equilibrium solutions in all cases is also studied. The regions of the basins of attraction for the equilibrium points of the present dynamical model for some values of the mass parameters are illustrated.

Equilibrium points and their stability in the restricted four-body problem

Periodic solutions in the Sun–Jupiter–Trojan Asteroid–Spacecraft system

In Long Term Evolution (LTE) networks initial cell planning strategy is essential to guarantee at cell edge appropriate minimum throughput, thus guarantee service minimum requirements. User throughput in uplink is affected mostly due to in-band interference which is created due to neighbor cells' capacity conditions. MAC Scheduler algorithm is the resource allocation function that allocates Resource Blocks (RB) in OFDM air interface to different users each unit of transmission time known as Time Transmission Interval (TTI). As a consequence in-band interference is produced by the number of users in the same RB in the same TTI in surrounding neighbor cells. Existing papers in international literature use mostly simulation results in graphical representation to simulate the interference vs. throughput conditions. However these simulations provide restrictions mostly based on the model assumptions. In this paper an uplink initial cell planning algorithm is proposed, using appropriate analytical mathematical models based on queuing theory, to predict overall interference. Using this analytical mathematical model cell planners could dynamically adjust their predictions to their individual assumptions, thus calculating uplink cell edge guaranteed throughput rate.

LTE cell coverage planning algorithm optimising uplink user cell throughput

This paper proposes a semi-analytical medium access control (MAC) layer model for the macroscopic analysis of long term evolution (LTE) uplink. The model takes into consideration the expected number of retransmissions arising from channel disturbances and the number of allocated resources so that to satisfy a required packet delay budget. The former is computed in terms of the mean bit error probability while the latter is calculated through a high order Markov chain incorporating cell traffic load conditions. The proposed model can be used as a macroscopic planning decision tool that poses the working limits of MAC schedulers for different packet delay budget requirements, in terms of the mean number of allocated resources, MAC packet length and maximum retransmission attempts according to the channel conditions. In this context, based on measured data, we investigate the impact of the MAC packet size on the total uplink delay budget of a single user aiming to set-up the basis for future multi-user analysis.

A. N. Baltagiannis

Papers

Equilibrium points and their stability in the restricted four-body problem

Families of periodic orbits in the restricted four-body problem

Periodic solutions in the Sun–Jupiter–Trojan Asteroid–Spacecraft system

LTE cell coverage planning algorithm optimising uplink user cell throughput

A Semi-Analytical Macroscopic MAC Layer Model for LTE Uplink