Impact of Geomagnetically Induced Currents on Power Transformers

This thesis deals with the impact of Geomagnetically Induced Current (GIC) on power transformers in electrical power systems. A simulator to calculate the flows of GIC in an electrical power network, based on an assumed or measured induced geoelectric potential is proposed. This simulator includes all needed mapping techniques to handle a system that cover a large geographical area. A correlation between GIC and the reactive power absorbed in the core of the saturated transformer is proposed. That correlation is used to estimate GIC in a transformer utilizing existing reactive power measuring infrastructure within the electrical grid without the need for dedicated measurement equipment. This technique is validated by simulations with electromagnetic transients software, laboratory work and through data recorded during a GIC event on the Hydro One network. The slope correlating reactive power absorption to GIC from an electromagnetic transient model of the transformer may be used to predict GIC levels in the actual transformers. The application of the technique correlating GIC with reactive power absorption is examined on a segment of a real 500 kV power transmission system. This technique allows GIC to be taken into account during load flow studies. Additionally, some benefits of increased visibility of GIC in the system are shown. A method to determine the frequency and magnitude of the harmonic currents generated by a saturated transformer is also proposed. It is expected that studies conducted in this thesis will be of value to utilities like Hydro One in planning mitigation measures against GICs

Uncertainty Quantification of Geo-Magnetically Induced Currents in UHV Power Grid

Geo-magnetically induced currents (GICs) have attracted more attention since many Ultra-High Voltage (UHV) transmission lines have been built, or are going to be built in the world. However, when calculating GICs based on the classical model, some input parameters, such as the earth conductivity and dc resistances of the grid, are uncertain or very hard to be determined in advance. Taking this into account, the uncertainty quantification (UQ) model of the geo-electric fields and GICs is proposed in this paper. The UQ of the maximums of the geo-electric fields and GICs during storms is carried out based on the polynomial chaos (PC) method. The results of the UHV grid, 1000 kV Sanhua Grid, were presented and compared to the Monte Carlo method. The total Sobol indices are calculated by using the PC expansion coefficients. The sensitivities of geo-electric fields and GICs to the input variables are analyzed based on the total Sobol indices. Results show that the GICs and geo-electric fields can be effectively simulated by the proposed model, which may offer a better understanding of the sensitivities to input uncertain variables and further give a reasonable evaluation of the geomagnetic threat to the grid

Geomagnetically induced currents (GIC) in large power systems including transformer time response

Includes bibliographical referencesGeomagnetically induced currents (GIC) are the result of changing geomagnetic fields which are a consequence of a geomagnetic disturbance (GMD). The flow of GIC through transmission lines and transformers across the power network could have severe consequences, if the magnitudes of the GIC are high enough. Problems that could arise from the flow of GIC in transmission networks include an increase in the amount of reactive power demand by GIC-laden transformers, half-wave saturation, excessive heating in transformers, incorrect operation of transmission line protection schemes and voltage collapse in affected sections of the network. In the past, GIC were calculated without taking the transformer's response time into account. The limitation of this approach is that the size and core type of the transformer is neglected. This may affect the assessment of GIC in the power network as the flux pattern and winding inductance distribution are not uniform across all transformer core structures. This thesis postulates that these characteristics could have far-reaching effects on the GIC that flows through a transformer as a function of time. Based on this assumption, a novel way of calculating GIC is introduced in this thesis. This method combines the uniform plane wave model and the network Nodal Admittance Matrix (NAM) method and incorporated for the first time, the transformer time response, which does not appear to have been considered in previous calculation methods. A general formula, which describes the transformer's time response to GIC was derived, followed by the derivation of the electric field induced in each transmission line. A key input to the prospective GIC with transformer time response calculation, is a set of piecewise linear equations derived from a laboratory test and PSCAD simulations. These suitably characterise the response of three transformer core structures, namely: bank of single phase (3(1P-3L)), three-phase three-limb (3P-3L) and three-phase five-limb transformers (3P-5L). Each of these core types were considered as a Generator Step-up Unit (GSU) and a Transmission Transformer (TT). The results of the laboratory experiment and simulations in PSCAD led to the conclusion that the transformer time response to GIC is irregular across the transformer cores that were tested. The 300 VA transformer core structure with the shortest response time is the 3P-3L, followed by the 3P-5L and the 3(1P-3L). For the 500 MVA transformers, the order was: 3P-3L; 3(1P-3L); and 3P-5L. The 3P-3L transformers permit the flow of GIC through the windings of the transformer over a shorter length of time. Therefore based on the order in response time, during GMDs leading to higher GIC, the prospective GIC with or without transformer time response flowing through 3P-3L transformers will be similar. Furthermore, the response time to GIC in 3P-3L, 3P-5L and 3(1P-3L) transformer core types are load-dependant. The 3(1P-3L) and 3P-5L transformers operating as TT's (modelled as transformers at 40 % load) have the longest response time to GIC, while 3P-3L transformers operating as a GSU (modelled as transformers at full load) have the longest response time to DC. The shortest response time to DC was with a GSU at light load (modelled as transformers at 80 % load), which was consistent across the three transformer core types. This correlates well with the notion that power networks could stand a better chance of surviving a high GMD when all generating units and loads are online. Three different core structures were modelled with a variation of DC current levels and load conditions, both in PSCAD and in the laboratory. These results are unique to the transformer models used, but are representative of major types of core configurations used on power networks. These results provide an indication that it is incorrect to lump the responses of all transformers and transformer time response should be taken into consideration, especially when sampling at intervals as low as 2 seconds

On the symmetry-preserving regularization model on complex flows using unstructured grids

Traditionally turbulence modeling of industrial flows in complex geometries have been solved using RANS models and unstructured meshes based solvers. The lack of precision of RANS models in these situations and the increase of computer power, together with the emergence of new high-efficiency sparse parallel algorithms, make possible the use of more accurate turbulent models such as Large Eddy Simulation models (LES). Recently, relevant improvements on turbulence modeling based on symmetry-preserving regularization models for the convective (non-linear) term have been developed. They basically alter the convective terms to reduce the production of small scales of motion by means of vortex-stretching, preserving all inviscid invariants exactly. To do so, symmetry and conservation properties of the convective terms are exactly preserved. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity can not blow up in the energy-norm (in 2D also: enstrophynorm). The numerical algorithm used to solve the governing equations must preserve the symmetry and conservation properties too. At this stage, results using regularization models at relatively complex geometries and configurations are of extreme importance for further progress. The main objective of the present paper is the assessment of regularization models on unstructured meshes. To do this, three different test cases have been studied: the impinging jet flow, the flow past a circular cylinder and a simplified Ahmed car. In order to analyse the influence of the filter, the cases have been solved using the Gaussian and the Helmholtz filters. Furthermore, the performance of the model considering the influence of the grid parameters and the filter ratio are also analysed.Peer ReviewedPostprint (published version

The Requirement and Formulation of a Gic-Inclusive State Estimator for Geomagnetic Disturbance Events

It is widely known that solar Coronal Mass Ejections (CMEs) emanating from the sun’s surface have the capacity to disturb the earth’s magnetic field. This leads to an event called a Geomagnetic Disturbance (GMD). The varying magnetic field caused due to this disturbance could result in an electric field over the earth’s surface. This electric field has the potential to eventually cause quasidc currents called Geomagnetically Induced Currents (GICs) circulating through the grid. When these quasi-dc currents flow through high-voltage transformers, they produce additional reactive power losses in them. Myriad research efforts have been taken to address the issue of circulating GICs from different perspectives. Improved GIC modelling, electric field estimation, GIC monitoring, stability analysis, and voltage study to list a few. But, none of the efforts have addressed the GMD problem from a Power System State Estimator (PSSE) perspective. PSSE is a tool employed by utilities in Energy Management Systems (EMS) and hence, is an important tool for making decisions pertaining to the grid. The additional reactive losses caused by GICs, being unaccounted for, could result in large deviations in the system states estimated. Therefore, my research is motivated by the lack of an accurate PSSE available for the utilities to be used during GMD events. A GIC-inclusive PSSE could greatly assist the utilities and system operators in taking operational decisions and hence, help in better management of the grid. The power grid is modelled as a dc system for GIC analysis and study. This is because GICs are quasi-dc and hence the system can be modelled as dc. Various studies that need to be carried out for GMD analysis require computation of transformer neutral GICs as well as other system parameters. A considerable portion of these studies are usually performed on MATLABR . But, there is no tool or package available on MATLAB that can provide easy and seamless calculations of these necessary parameters. One direct example, relevant to my thesis, of an application of such a tool, would be in the modified PSSE itself. The modified PSSE would require the calculation of transformer neutral GICs. Therefore, another research motivation is the construction of an efficient tool for the calculation of such system values that could be utilized for various GMD studies. For my research, the accuracy of the traditional state estimator was checked for GMD events. This state estimator failed to produce accurate results during the GMD events and accumulated noticeable results. To solve this problem, the GIC-Inclusive state estimator was constructed using the GMD tool, MATGMD. This modified state estimator was successful in obtaining accurate results for the EPRI 20 bus case and the UIUC bus case with the error in the voltage magnitude states in the range of 10^-5 and for the neutral current states in the range of 10^-4. The results for the EPRI 20 bus case using the GIC-Inclusive state estimator have been depicted and comparisons with the traditional state estimator have been made. The GIC-Inclusive state estimator, though computationally heavy, is very effective and the advantages of its applications outweighs the ease of using the traditional state estimator during GMD events

Estimation of Geomagnetically Induced Currents (GICS) in the Namibian transmission network

Includes bibliographical references.Geomagnetically Induced Currents (GICs) have become a matter of concern not only to networks located in high magnetic latitude regions but also in networks located in mid-latitude regions. GICs pose a threat of transmission equipment damage which could lead to short power interruptions and potentially long term blackouts. Improved modelling techniques are essential in predicting the GICs flowing in the network in order to enable power utilities to reduce the risk of damage to equipment and improve the reliability of their power supply. This dissertation, entitled ESTIMATION OF GEOMAGNETICALLY INDUCED CURRENTS (GICS) IN THE NAMIBIAN TRANSMISSION NETWORK, aims at improving GIC estimation by installing measurement equipment in order to compare measured GIC results with modelled results. The purpose of which is to validate the calculation technique. The Nodal Admittance technique was proposed for the study and was first validated using published data obtained using the a&b parameter method. For the measurement techniques, two methods were found namely direct measurements in the transformer neutral conductor and indirect measurements in the transmission lines. In this dissertation, the former was implemented due to its simplicity in usage

Second order quasilinear PDEs in 3D: integrability, classification and geometric aspects

In this work we apply the method of hydrodynamic reductions to study the integrability of the class of second order quasilinear equations [continues…

The Effects of Preference Characteristics and Overconfidence on Economic Incentives

This dissertation is a collection of three independent research papers and three chapters with surveys introducing into the respective literature. The first paper analyses the effects of introducing Inequity Aversion in a Moral Hazard Problem, the second paper is about optimal delegation in groups involved in contests, and the third paper is about the optimal delegation decision of firms who can hire possibly overconfident managers.Incentives; Inequity Aversion; Contracts; Strategic Delegation; Overconfidence

Enhanced power system resiliency to high-impact, low-frequency events with emphasis on geomagnetic disturbances

Various reliability procedures have been developed to protect the power systems against common reliability issues that threaten the grid frequently. However, these procedures are unlikely to be sufficient for high-impact low-frequency (HILF) events. This thesis proposes several techniques to enhance resiliency with respect to HILF events. In particular, we focus on cyber-physical attacks and geomagnetic disturbances (GMDs). Corrective control through generation redispatch is proposed to protect the system from cyber-physical attacks. A modification of the optimal power flow (OPF) is proposed which optimizes the system resiliency instead of the generation cost. For larger systems, the burden of solving the resilience-oriented OPF is reduced through a fast greedy algorithm which utilizes proper heuristics to narrow the search space. Moreover, an effective line switching algorithm is developed to minimize the GMD impact for large-scale power systems. The algorithm uses linear sensitivity analysis to find the best switching strategy and minimizes the GIC-saturated reactive power loss. The resiliency may be improved through power system monitoring and situational awareness. Power system data is growing rapidly with the everyday installation of different types of sensors throughout the network. In this thesis, various data analytics tools are proposed to effectively employ the sensor data for enhancing resiliency. In particular, we focus on the application of real data analysis to improve the GMD models. We identify common challenges in dealing with real data and develop effective tools to tackle them. A frequent issue with model validation is that for a real system, the parameters of the model to be validated may be inaccurate or even unavailable. To handle this, two approaches are proposed. The first approach is to develop a validation framework which is independent of the model parameters and completely relies on the measurements. Although this technique successfully handles the system uncertainties and offers a robust validation tool, it does not provide the ability to utilize the available network parameters. Sometimes, the network parameters are partially available with some degree of accuracy and it is desired to take advantage of this additional information. The second validation framework provides this capability by first modifying the model to account for the missing or inaccurate parameters. Then a suitable validation framework is built upon that model. Another common issue that is widely encountered in data analysis techniques is incomplete data when part of the required data is missing or is invalid. Examples of missing data are provided through real case studies, and advanced imputation tools are developed to handle them

Synthesis of finite displacements and displacements in continental margins

The scope of the project is the analysis of displacement-rate fields in the transitional regions between cratonal and oceanic lithospheres over Phanerozoic time (last 700 ma). Associated goals are an improved understanding of range of widths of major displacement zones; the partition of displacement gradients and rotations with position and depth in such zones; the temporal characteristics of such zones-the steadiness, episodicity, and duration of uniform versus nonunifrom fields; and the mechanisms and controls of the establishment and kinematics of displacement zones. The objective is to provide a context of time-averaged kinematics of displacement zones. The initial phase is divided topically among the methodology of measurement and reduction of displacements in the lithosphere and the preliminary analysis from geologic and other data of actual displacement histories from the Cordillera, Appalachians, and southern North America