Grid Visibility Research Articles

Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs (USGV), an alternative characterisation of the well-known rectilinear graphs. We extend known combinatorial results for USGV and we show that, in the weak case (i.e., visibilities do not necessarily translate into edges of the represented combinatorial graph), the area minimisation variant of their recognition problem is {{,mathrm{{textsf{N}}{textsf{P}}},}}-hard. We also provide combinatorial insights with respect to USV, and as our main result, we prove their recognition problem to be {{,mathrm{{textsf{N}}{textsf{P}}},}}-hard, which settles an open question.

From smart grid events to a proactive fault approach

Advanced Metering Infrastructure is nowadays the main data input to support a proactive low voltage smart grid operation, with a high capability of adding sustained value not only to the lower voltage level but also creating important triggers that can enhance medium voltage grid visibility. Several functions are already on the productive stage at E-REDES systems enabling fair visibility about the impact of distributed energy resources, load balance regarding the rising impact of electrical mobility, and in a near future the non-linearities coming from microgrids and flexibility markets. To achieve the operational goals, it isn't enough to deploy smart meters, neither to have (near) real-time visualization on assets spread through the grid, it is mandatory to know the location of the constraints and which actions should be performed to provide the most efficient action plan to solve the constraint without causing unforeseen impacts on service continuity and quality of service. This paper shows a strategy to handle the increasing number of data nodes like smart meters and distributed energy manageable resources. The challenges are set on how to capitalize value from data computed as information and addressed as knowledge enabling proactive actions on grid constraints, even before customers can report them. Control room engineers are now able to look at a list, that uses on the background algorithms to convert events coming from low voltage smart grids, into value-adding alarms, due to evolutions made on two concepts, the event aggregation process and the common node approach. To guide control room engineers on how to take a standard approach to different alarms, three decision-making processes were developed and tested in a real operational environment, generating a high success rate on field crew proactive dispatch.

Frequency Selective Auto-Encoder for Smart Meter Data Compression.

With the development of the internet of things (IoT), the power grid has become intelligent using massive IoT sensors, such as smart meters. Generally, installed smart meters can collect large amounts of data to improve grid visibility and situational awareness. However, the limited storage and communication capacities can restrain their infrastructure in the IoT environment. To alleviate these problems, efficient and various compression techniques are required. Deep learning-based compression techniques such as auto-encoders (AEs) have recently been deployed for this purpose. However, the compression performance of the existing models can be limited when the spectral properties of high-frequency sampled power data are widely varying over time. This paper proposes an AE compression model, based on a frequency selection method, which improves the reconstruction quality while maintaining the compression ratio (CR). For efficient data compression, the proposed method selectively applies customized compression models, depending on the spectral properties of the corresponding time windows. The framework of the proposed method involves two primary steps: (i) division of the power data into a series of time windows with specified spectral properties (high-frequency, medium-frequency, and low-frequency dominance) and (ii) separate training and selective application of the AE models, which prepares them for the power data compression that best suits the characteristics of each frequency. In simulations on the Dutch residential energy dataset, the frequency-selective AE model shows significantly higher reconstruction performance than the existing model with the same CR. In addition, the proposed model reduces the computational complexity involved in the analysis of the learning process.

Synergizing PMU Data From Multiple Locations in Indian Power Grid-Case Study

Synchrophasor technology improves power grid visibility by installing phasor measurement units (PMUs) over a wide area in the power system. Big data received from PMUs contains important information about grid behavior. This information is useful in monitoring the safety and security of the grid. An extensive state-of-the-art review of big data analytics and its prime applications in power systems are expressed in this paper. It presents, a general background in data analysis techniques such as exploratory data analysis, statistical data analysis, and unsupervised data mining techniques like clustering. Two 400 kV transmission line tripping events are analyzed from the data recorded by the PMUs installed in the western part of the Indian grid i.e., Maharashtra State Electricity Transmission Company Limited (MSETCL) grid. The box plots, Correlogram, and the formation of clusters carried out for the PMU data recorded under ambient and disturbance events. This provides insights on how effective big data helps to make the right decision at right time for effective management of the power grid under normal and contingency conditions.

Software Defined Communication Network Reliability for Secondary Distribution Power Grid

Operations automation of Secondary Distribution Electrical Power Grid (SDEPG) requires reliable communication network to facilitate end to end power grid visibility and control through various sensors and actuators deployed across the power grid network. Available solutions to enhance communication network reliability have addressed mostly requirements for transmission and primary distribution portions of the grid, which use wired communication network technologies. The nature of SDEPG demands reliability solutions to incorporate a combination of wired and wireless technologies. In this research we propose an SDN based, cross layers resilient communication network for SDEPG. The solution segments the SDEPG into three parts, namely access, aggregation and core networks. Since aggregation and core comprises of wired network, we adopt the resilience approach proposed by previous researchers. As for access network that is largely comprised of wireless network, we propose an algorithm that modifies the Radio Frequency (RF) parameters of failover Access Points (AP) to optimally cover abandoned clients when the serving AP fails. The proposed solution was simulated using OPNET, that contain NS3 for the network simulation and mininet for SDN and was deployed in virtualized HP server. The simulation comprised of two access points and two stations. Traffic flow was initiated between two stations. With different failure scenarios simulated, our results revealed that in case of Access Point (AP) failure, the SDN controller seamlessly redirects users to a nearby AP while maintaining acceptable bandwidth, latency and availability

NeuralCompression: A machine learning approach to compress high frequency measurements in smart grid

The smart grid features frequent communication of measurements collected at consuming and distributing nodes to other agents in the grid. While this increases grid visibility and improves situation awareness, the sheer volume of such data generated from the geographically vast grid will result in overloading of the communication infrastructure. In this regard, compressing data at the source and communicating compressed measurements has been explored in the literature. However, such techniques rely on the presence of a structure in data that is exploited for compression. In this article we propose the use of Autoencoder for data compression that extracts an appropriate structure from data that then allows for compression. The proposed approach also incorporates nonlinear transformations in the compression mechanism which is likely to improve the compression ratio for the same reconstruction accuracy. The proposed method is applied on four publicly available datasets and results show that the Autoencoder has merit over state-of-the-art Compressive Sensing for high compression ratios. Generalization of Autoencoder models to datasets from different geographical locations is also studied as a distinct feature of the proposed method. The generalizability of models is also improved with transfer learning by adapting pre-trained models to the idiosyncrasies of target dataset.

Vulnerability Analysis of Smart Grids to GPS Spoofing

Sensors such as phasor measurement units (PMUs) endowed with GPS receivers are ubiquitously installed providing real-time grid visibility. A number of PMUs can cooperatively enable state estimation routines. However, GPS spoofing attacks can notably alter the PMU measurements, mislead the network operator, and drastically impact subsequent corrective control actions. Leveraging a novel measurement model that explicitly accounts for the GPS spoofing attacks, this paper formulates an optimization problem to identify the most vulnerable PMUs in the network. A greedy algorithm is developed to solve the aforementioned problem. Furthermore, the paper develops a computationally efficient alternating minimization algorithm for joint state estimation and attack reconstruction. Numerical tests on IEEE benchmark networks validate the developed methods.

Visibility Drawings of Plane 3-Trees with Minimum Area

A visibility drawing of a plane graph G is a drawing of G where each vertex is drawn as a horizontal line segment and each edge is drawn as a vertical line segment such that the line segments use only grid points as their endpoints. The area of a visibility drawing is the area of the smallest rectangle on the grid which encloses the drawing. A minimum-area visibility drawing of a plane graph G is a visibility drawing of G where the area is the minimum among all possible visibility drawings of G. The area minimization for grid visibility representation of planar graphs is NP-hard. However, the problem can be solved for a fixed planar embedding of a hierarchically planar graph in quadratic time. In this paper, we give a polynomial-time algorithm to obtain minimum-area visibility drawings of plane 3-trees.

Towards area requirements for drawing hierarchically planar graphs

Hierarchical graphs are an important class of graphs for modeling many real applications in software and information visualization. In this paper, we investigate area requirements for drawing hierarchically planar graphs regarding two different drawing standards. Firstly, we show an exponential lower bound for the area needed for straight-line drawing of hierarchically planar graphs. The lower bound holds even for s- t hierarchical graphs without transitive arcs, in contrast to the results for upward planar drawing. This motivates our investigation of another drawing standard grid visibility representation, as a relaxation of straight-line drawing. An application of the existing results from upward drawing can guarantee a quadric drawing area for grid visibility representation but does not necessarily guarantee the minimum drawing area. Motivated by this, we will present a new grid visibility drawing algorithm which is efficient and guarantees the minimum drawing area with respect to a given topological embedding. This implies that the area minimization problem is polynomial time solvable restricted to the class of graphs whose planar embeddings are unique. However, we can show that the problem of area minimization of grid visibility for hierarchically planar graphs is generally NP-hard, even restricted to s- t graphs.