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Difference methods are widely used for the approximate solution of boundary value problems for partial differential equations. Grid approximations are most simply constructed when the computational domain is divided into rectangular cells. Typically, the grid nodes coincide with the vertices of the cells. In addition to such node-center approximations, grids with nodes at the centers of cells are also used. It is convenient to formulate boundary value problems in terms of invariant operators of vector (tensor) analysis, which are associated with corresponding grid analogs. In this work, analogs of the gradient and divergence operators are constructed on non-standard rectangular grids the nodes of which consist of both the vertices of the computational cells and their centers. The proposed approach is illustrated using approximations of a boundary value problem for a stationary two-dimensional convection–diffusion equation. The key features of constructing approximations for vector problems are discussed with a focus on applied problems of the mechanics of solids. [ABSTRACT FROM AUTHOR]

The smart grid is enabling the collection of massive amounts of high-dimensional and multi-type data about the electric power grid operations, by integrating advanced metering infrastructure, control technologies, and communication technologies. However, the traditional modeling, optimization, and control technologies have many limitations in processing the data; thus, the applications of artificial intelligence (AI) techniques in the smart grid are becoming more apparent. This survey presents a structured review of the existing research into some common AI techniques applied to load forecasting, power grid stability assessment, faults detection, and security problems in the smart grid and power systems. It also provides further research challenges for applying AI technologies to realize truly smart grid systems. Finally, this survey presents opportunities of applying AI to smart grid problems. The paper concludes that the applications of AI techniques can enhance and improve the reliability and resilience of smart grid systems.

Variable renewable generation technologies such as wind and solar photovoltaic have introduced new challenges in power system management. Grid operators have traditionally used ancillary services such as reserve and reactive power to help to maintain a secure and reliable power system. In addition, conventional synchronous generators have inherent characteristics such as inertial response, which help the power system to recover after an event. In Ireland and Northern Ireland, a weakly‐interconnected island system with a high penetration of wind, new ancillary or 'system' services have been devised to address the technical scarcities arising from the displacement of synchronous generation. Twelve system services addressing the frequency and voltage control needs have been procured to date, allowing the power system to be operated with up to 65% instantaneous non‐synchronous renewable power on the system. This study outlines the implementation of the innovative system services framework. It includes an overview of the services procured and examples of the changed behaviour of existing units in response to financial incentives. It also examines how new technologies have responded to the signals provided, questions how aspects of the arrangements may be further improved and details the challenges of integrating the use of these innovative services into operational policy. [ABSTRACT FROM AUTHOR]

This study examines experiences of grid operators to successfully integrate very high penetrations of wind and solar photovoltaic (PV) resources. The variability of these resources creates challenges in balancing the system generation and demand, and ensuring resource adequacy and essential reliability services. The inverter‐based nature of wind and solar PV leads to challenges in frequency, transient, and small‐signal stability. In this study, seven system operators demonstrate the ability to manage these challenges in a variety of power systems, from stand‐alone island systems to larger island systems that are interconnected to neighbours, to balancing authorities that are strongly interconnected within very large synchronous systems. They operate within a variety of market constructs, from full regional transmission operators to vertically‐integrated utilities. All are experiencing increases in the penetration of inverter‐based, variable energy resources and finding creative solutions to these challenges. [ABSTRACT FROM AUTHOR]

• Grid operators have been active in the energy transition through the development of decentralized energy innovations. • Their public mandate, broad access to the grid and markets, and regulatory misalignment motivate their (embedded) agency. • They perform all three types of institutional work and use the same practices for diverse purposes. • They use their agency for institutional change through the creation of niches and boundary spanning. • They are both object and subject of institutional work in a distributed, collective process of institutional change. The agency of incumbents has gained increasing attention in the study of transitions. Recent studies show that besides being inert and resistant to change, incumbents can also support transitions. We focus on the agency of a particular type of incumbent, grid operators. In several countries, these actors play an active role in institutional change in the energy domain. At the same time, they are engaging in activities to maintain the regime. This paper examines the actions of grid operators when performing institutional work, i.e. when creating, maintaining and disrupting institutions. We conducted a qualitative content analysis of Dutch media to analyze the actions of grid operators while engaging with decentralized energy innovations. We conclude that grid operators are both subject and object of institutional work as part of a distributed, collective process of institutional change. Furthermore, our analysis reflects on their paradoxical position as embedded actors engaging in institutional change. [ABSTRACT FROM AUTHOR]

During the last two decades, the use of residential photovoltaic (PV) systems has been widely promoted by governments through various support mechanisms such as feed‐in‐tariffs, net‐metering, net‐billing, etc. These support schemes have developed a secure investment environment, increasing the penetration level of PVs in low‐voltage distribution grids. Nonetheless, increased PV integration may introduce several technical problems regarding the secure operation of distribution grids. Battery energy storage (BES) systems can mitigate such challenges, but the high capital cost is one of the most important limiting factors towards the widespread use of these systems. In fact, the financial viability of integrated PV and BES systems under different support schemes remains an open issue. In this study, the profitability of PV and BES systems is evaluated through an advanced techno‐economic model, that provides the optimal size of PV‐BES system in terms of net present value, based on the electricity production and consumption profile of the installation, PV and BES systems costs, and electricity charges. The proposed model may be a useful tool for prosumers, grid operators and policymakers, to assess the impact of various incentive policy schemes and different BES operation strategies on the economic viability of PV‐BES systems. [ABSTRACT FROM AUTHOR]

A grid analog of the formula of integration by parts is constructed and studied for a two-dimensional case in which one of the grid functions is defined at nodes, and the second function is defined at the midpoints of the sides of cells of a simplicial grid in the Cartesian and cylindrical systems of coordinates. Grid analogs of such first-order differential operators as the gradient, divergence, and curl operators, can be naturally defined using this formula. [ABSTRACT FROM AUTHOR]

Grid operation becomes a more challenging task due to the increasing amount of distributed generators in the system. Consequently, critical situations with violations of operational limits occur more frequently. Hence, grid operators have to take corrective countermeasures to ensure the security of supply. This study presents a discrete optimisation approach to determine the optimal amount of distributed generator curtailment regarding multiple objectives. The proposed method is based on non‐linear AC load flow analysis of the network. The method is implemented into a modified version of the IEEE 14‐bus test system and the necessary amount of generation curtailment to retain predefined operational limits is identified. Simulations are carried out for different contingency scenarios and several possible increments of curtailment levels are compared. Results reveal the potential to reduce the total amount of power adjustments distinctly by using curtailment levels with smaller step sizes compared to todays' applied standards in German grid operation. Furthermore, the developed methodology enables distributed generators to be used for managing congestions of transformers connecting different voltage levels. [ABSTRACT FROM AUTHOR]

The inertia of power systems is a key aspect of frequency dynamics and stability. The increasing penetration of non‐synchronous generation reduces the available inertia and makes it fluctuating during the day depending on the online units. This causes problems for grid operators, particularly in relatively small power systems. The present work examines the impact of decreasing inertia using an aggregate model based on the swing equation, considering future lower inertia scenarios and the implementation of the current protection schemes. The frequency stability of the system is assessed by considering the reference incident, i.e. the loss of the largest operating unit in under‐ and over‐frequency cases. New solutions to balance the grid are addressed and compared, considering the technical impacts of synchronous compensators and battery energy storage systems (BESSs) operated with a new equivalent saturation logic. The model is tested and validated using the real data of a small insular power system (Sardinia Island, Italy), outlining the importance of the high‐voltage direct current and of the BESS control strategies to guarantee the frequency stability of the power system. [ABSTRACT FROM AUTHOR]

For stationary diffusion-type equations, we study the convergence of grid inhomogeneous boundary-value problems of a version of the mimetic finite difference (MFD) technique in which grid scalars are defined inside grid cells and grid vectors are specified by their local normal coordinates on the plane faces of grid cells. Grid equations and boundary conditions are formulated in operator form using consistent grid analogs of invariant first-order differential operators and of boundary operators. Convergence is studied on the basis of the theory of operator difference schemes; i.e., a priori estimates for the norm of the solution error in terms of the norm of the approximation error are obtained that guarantee convergence of the first order under inhomogeneous boundary conditions of the first, second, and third kind in a domain with a curvilinear boundary. Grid analogs of embedding inequalities and approximation relations obtained earlier are used. [ABSTRACT FROM AUTHOR]

In future power systems with little system inertia, grid operators will require the provision of synthetic inertia (SI) from renewable energy sources. Unlike today, grid operators may require continuous provision of SI. This can lead to an unwanted disconnection of wind turbine generators (WTGs) from the grid, and has the potential to cause a significant decrease of the energy yield and financial losses for the turbine operator. In order to avoid such situations a controller is proposed, which interprets the grid codes to the benefit of all parties involved. This can be achieved by a variable inertia constant, which changes with the operating point of the WTG. In this study, the behaviour of the variable inertia constant controller is described, assessed and verified with time domain simulations. [ABSTRACT FROM AUTHOR]

Using grids (meshes) formed from polyhedra (polygons in the two-dimensional case), we consider differential and boundary grid operators that are consistent in the sense of satisfying the grid analog of the integral identity - a corollary of the formula for the divergence of the product or a scalar by a vector. These operators are constructed and applied in the Mimetic Finite Difference (MFD) method, in which grid scalars are defined inside the grid cells and grid vectors are defined by their local normal coordinates on the planar faces of the grid cells. We show that the basic grid summation identity is a limit of an integral identity written for piecewise-smooth approximations of the grid functions. We also show that the MFD formula for the reconstruction of a grid vector field is obtained by approximation analysis of the summation identity. Grid embedding theorems are proved, analogous to well-known finite-difference embedding theorems that are used in finite-difference scheme theory to derive prior bounds for convergence analysis of the solutions of finite-difference nonhomogeneous boundary-value problems. [ABSTRACT FROM AUTHOR]

Sensors are gaining a ubiquitous status over many application domains with regard to enabling data‐driven decision making and smart functionality. Integration of sensors with cloud‐based data storage and analysis has the potential to significantly enhance the efficiencies, resilience and adaptability of managing smart infrastructure management. In this context, a standout application is smart grid, which provides an electricity delivery service with the ability to monitor, protect and optimize various operations of its connected elements from service provider to consumer. An ability to read and manage smart grid measurements remotely using wireless sensors is an important advantage that allows the grid operators to balance loads effectively and enable on‐demand services for various entities. However, the adoption of cloud infrastructure to manage sensor data in a smart grid poses significant risks to data security and consumers privacy. The data maybe exposed to malicious or unwarranted parties, with the potential for various security attacks that may impact data integrity, availability and accountability. We propose a secure and practical billing model using homomorphic encryption within a cloud‐based data processing framework. Moving billing management into the cloud securely, with on‐demand data retrieval and statistical computations is a major strength of the proposed framework. [ABSTRACT FROM AUTHOR]

Properties of a version of MFD method are studied for a grid problem on a polyhedral grid in which the grid scalars are defined on grid cells and the grid flows are specified by their local normal coordinates on the plane faces of cells. In a domain with curvilinear boundary, a grid inhomogeneous boundary value problem for stationary diffusion-type equations is considered. An operator statement of the grid problem is given, and a local approximation of the equations and boundary conditions is studied. [ABSTRACT FROM AUTHOR]

With the growing penetration of renewable energy resources, the grid operators place higher emphasis on their grid integration requirements. The low-voltage ride-through (LVRT) capability is one of the most important issues for maintaining the grid stability. This paper proposes a LVRT technique for effective utilization of the ampere capacity of the grid-connected converter to meet the LVRT requirement, and to reduce the potential post-sag inrush current of the transformer within the grid-connected converter system. This technique precisely manages the peak value of converter's phase current while performing the transformer flux compensation and the current injection for full utilization of the ampere capacity without the risk of triggering the overcurrent protection. The operation principles of the proposed method is explained, and laboratory test results are presented for validation. [ABSTRACT FROM AUTHOR]

The implementation of online dynamic security assessment (DSA) systems is growing worldwide, and the deployment of this advanced technology is expected to improve the real-time security and, hence, the reliability of power systems. While not insignificant, the cost and efforts required to install online DSA tools are minor compared to the benefits of reducing the volume of offline studies required and, more importantly, the benefits of identifying and avoiding potential security problems in the systems to reduce the risk of blackouts. Based on practical experience, a process of DSA system integration is presented that can assist utilities and grid operators in addressing key issues during the specification, development, and installation of such tools. A number of successful online DSA projects are discussed to illustrate the viability and practicality of such applications, even for large, complex power systems. The penetration of online DSA tools is expected to continue to grow as operators seek timely and cost-effective approaches to enhance system performance. In the meantime, work is continuing on new methods of online analysis, advanced preventive and corrective control tools, and improved hardware architectures [ABSTRACT FROM PUBLISHER]

A major drawback of current dynamic security assessment (DSA) software used to analyze the transient and dynamic responses to a large number of potential power system disturbances in a transient time frame is the long simulation time required to complete the calculations, making it impractical for real-time applications. This paper describes an attempt to dramatically reduce the time for DSA calculations so that DSA analyses can be converted from offline studies to routine, online use to aid grid operators in their real-time controller analyses. Using a new distributed computational architecture among other techniques, a modified version of DSA is developed which performs calculations fast enough for real-time applications to energy management systems (EMS) that operate today's grid systems. [ABSTRACT FROM PUBLISHER]