This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Today, the stability of the electric power grid is maintained through real time balancing of generation and demand. Grid scale energy storage systems are increasingly being deployed to provide grid operators the flexibility needed to maintain this balance. Energy storage also imparts resiliency and robustness to the grid infrastructure. Over the last few years, there has been a significant increase in the deployment of large scale energy storage systems. This growth has been driven by improvements in the cost and performance of energy storage technologies and the need to accommodate distributed generation, as well as incentives and government mandates. Energy management systems (EMSs) and optimization methods are required to effectively and safely utilize energy storage as a flexible grid asset that can provide multiple grid services. The EMS needs to be able to accommodate a variety of use cases and regulatory environments. In this paper, we provide a brief history of grid-scale energy storage, an overview of EMS architectures, and a summary of the leading applications for storage. These serve as a foundation for a discussion of EMS optimization methods and design.

Energy Management and Optimization Methods for Grid Energy Storage Systems

Higher cost and stochastic nature of intermittent renewable energy (RE) resources complicate their planning, integration and operation of electric power system. Therefore, it is critical to determine the appropriate sizes of RE sources and associated energy storage for efficient, economic and reliable operation of electric power system. In this study, two constraint-based iterative search algorithms are proposed for optimal sizing of the wind turbine (WT), solar photovoltaic (PV) and the battery energy storage system (BESS) in the grid-connected configuration of a microgrid. The first algorithm, named as sources sizing algorithm, determines the optimal sizes of RE sources while the second algorithm, called as battery sizing algorithm, determines the optimal capacity of BESS. These algorithms are mainly based upon two key essentials, i.e. maximum reliability and minimum cost. The proposed methodology aims to avoid over- and under-sizing by searching every possible solution in the given search space. Moreover, it considers the forced outage rates of PV, WT and utilisation factor of BESS which makes it more realistic. Simulation results depict the effectiveness of the proposed approach.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-rpg.2017.0010

Optimal sizing of a wind/solar/battery hybrid grid-connected microgrid system

This paper introduces a novel approach for optimal operation of distribution networks at the presence of distributed generation resources and battery energy storage system. Modern power distribution networks must operate not only at the most economical way but also at a reasonable level of system reliability. Toward this end a special attention has been paid to reliability assessment in which turns the proposed problem into a multiobjective energy management (MOEM). Energy not supplied, a prominent reliability index, is considered as an objective function beside the operation cost. A hybrid evolutionary algorithm, hybrid grey wolf optimizer-particle swarm optimization algorithm, is also proposed to solve the proposed MOEM. Accuracy of the proposed algorithm is evaluated on IEEE 84-bus standard distribution system. Obtained results are compared with those available in literatures to prove the supremacy of the proposed algorithm. Furthermore, a benefit analysis has been done to assess the associated cost of the photovoltaic installment.

A New Bi-Objective Approach to Energy Management in Distribution Networks with Energy Storage Systems

ower transformers are one of the most expensive elements in a power system, and their failure is a very costly event. Power transformers are mainly involved in energy transmission and distribution. Unplanned power transformer outages have considerable economic impact on the operation of electric power networks. To have reliable operation of transformers, it is necessary to identify problems at an early stage before a catastrophic failure occurs. In spite of corrective and predictive maintenance, preventive maintenance is gaining due importance in the modern era, and it must be taken into account to obtain the highest reliability of power apparatus such as power transformers. The well-known preventive maintenance techniques such as dissolved gas analysis (DGA), thermal monitoring, partial discharge measurement, capacitance and tan delta measurements, frequency response analysis, etc. are performed on transformers for a specific type of problem. DGA is a very efficient and reliable tool for the earliest detection of inception faults in transformer and other electrical equipment using insulating oil. Condition monitoring of electrical equipment, such as transformers, helps users in many ways such as planning of maintenance schedule, obtaining knowledge of the health of equipment, estimating the remaining service life of equipment, finding areas of further improvement, refining product specification, etc. Kraft paper (cellulose) immersed in mineral oil is used as the insulation system for the copper windings in large power transformers. As the system ages under load, the paper and oil can degrade, potentially leading to catastrophic failure. Partial discharge (PD) is an important tool for improving the reliability of HV insulation systems. It is a very sensitive and nondestructive method of evaluation of the health of the insulation of any HV equipment. PD always is associated with the degradation of insulation systems in HV equipment. Therefore, PDs need to be detected, measured, located, and reduced to a safe value so that the quality of the insulation system is not affected.

Condition Monitoring of Power Transformers - Bibliography Survey

Prompted by technical issues that have arisen due to the widespread deployment of distributed intermittent renewable generators, rapidly rising peak demand and reductions in battery price, the use of battery-based energy storage systems in power networks is on the rise. While battery-based energy storage has the potential to deliver technical benefits, the best possible sizing, location and usage govern the financial viability. The objective of this study is twofold. Firstly, a generalised approach is proposed to model network upgrade deferral as a function of load growth rate, renewable generation penetration and peak shave fraction. This model is then used for the formulation of an optimisation problem which benefits from multi-period power flow analysis to co-optimise battery size, location, charge/discharge profile for a pre-specified number of units to be deployed in a given distribution network. The proposed approach is implemented using the generic algebraic modelling system platform and validated on an Australian medium voltage distribution network under multiple practical and potential future scenarios.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-rpg.2015.0440

Evaluation of technical and financial benefits of battery-based energy storage systems in distribution networks

Dielectric testing techniques, in both time and frequency domains are currently being widely used by the power utilities for the assessment of the condition of transformer oil-paper insulation systems. However, it has been reported that the results of these tests are highly influenced by the operating temperature during the measurement. The distribution, migration and equilibrium of moisture between oil and paper in a complicated insulation system are highly temperature dependent. It requires adequate experience and proper understanding to interpret the dielectric response results in the presence of temperature variations and thermal instability. Proper analysis of the dielectric test result is only possible with a thorough understanding of the physical behaviour of the insulation system in response to temperature. Frequency domain dielectric spectroscopy (FDS) has been investigated for a model transformer at different operating temperatures. FDS data was then used to simulate polarization and depolarization currents. A correlation has been investigated between the operating temperature and FDS measured data, which is then extended to simulated PDC data. Finally the problems of a clear and transparent interpretation of the dielectric test results have been explained.

Impact of temperature on the frequency domain dielectric spectroscopy for the diagnosis of power transformer insulation

Water tree degradation in underground XLPE insulated cables is a growing, worldwide problem. This form of degradation is ultimately fatal for affected cables, and therefore the detection of damaging trees in power cable insulation is vital for distribution companies to avoid catastrophic failure. Dielectric response measurements, in both the time and frequency domains, can generate valuable information about the condition of the cable. However, the interpretation of how these dielectric response measurements relate to water tree density and length is a difficult task. This paper will present a new dielectric response model for water tree degraded XLPE insulation. The model is based on finite element analysis to determine the electrical behaviour of water tree degraded insulation. Preliminary simulations will verify the model development by comparing the results to small sample pulsed electro-acoustic (PEA) measurements performed by other researchers. The importance of a strong non-linearity mechanism for accurate modelling will also be elucidated.

A new dielectric response model for water tree degraded XLPE insulation - part a: model development with small sample verification

Preventive diagnosis and maintenance of transformers has become more and more useful in recent times in order to improve the reliability of electric power systems. Time domain dielectric testing techniques such as Return Voltage (RV) measurement and Polarisation-Depolarisation Current (PDC) measurement have recently been widely used as potential tools for condition assessment of transformer insulation. In the frequency domain, measurement of the dissipation factor (tanδ) over a frequency range of 0.1 mHz to 1 kHz has been commonly used to assess the condition of transformer insulation. A number of transformers have been tested with these diagnostic techniques. A better understanding and analysis of the dielectric test results is only possible with a clear understanding of the physical behaviour of the insulation system in response to moisture and ageing. A circuit model, which describes the dielectric behaviour of the transformer's main insulation system, has been modelled in this paper from the frequency domain measurement data and then RV and PDC data have been simulated from the circuit model. This paper then presents discussions of frequency and time domain techniques to find the condition of transformer insulation in terms of moisture and ageing estimation.

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Understanding frequency & time domain polarisation methods for the insulation condition assessment of power transformers

Dielectric response measurements, in both time and frequency domains, can generate valuable information about the condition of cables affected by water tree degradation. However, the interpretation of how these dielectric response measurements relate to water tree density and length is a difficult task. This difficulty in assessing in particular the longest water tree length from dielectric response measurements is a substantial limitation, as it is well known that the remaining electrical strength of a water tree degraded cable is related to the longest tree length. This paper will detail a study whose goal was to enhance the understanding of how water tree degradation (in particular long vented trees) influences the dielectric response, and therefore seeks to reduce this interpretation limitation. The paper examines the application of a finite element model for water tree degraded insulation. This application involves using the dynamic electrical behavior as predicted by the model to generate frequency domain dielectric responses. The predicted electrical behaviour of both bow-tie and vented trees and the dielectric response that such trees will produce is examined and compared to actual Frequency Domain Spectroscopy (FDS) measurements on water tree degraded cable samples. It is shown that the developed model can accurately reproduce such measurement behavior, including the non-linear response. Because of the success of the model in reproducing actual dielectric response measurements of water tree degraded cables, it has proven itself to be a useful interpretive tool for water tree detection and assessment.

Andrew Thomas

Papers

Evaluation of technical and financial benefits of battery-based energy storage systems in distribution networks

Impact of temperature on the frequency domain dielectric spectroscopy for the diagnosis of power transformer insulation

A new dielectric response model for water tree degraded XLPE insulation - part a: model development with small sample verification

Understanding frequency & time domain polarisation methods for the insulation condition assessment of power transformers

A new dielectric response model for water tree degraded XLPE insulation - part b: dielectric response interpretation