Design Exploration of an FPGA-Based Multivariate Gaussian Random Number Generator

Monte Carlo simulation is one of the most widely used techniques for computationally intensive simulations in a variety of applications including mathematical analysis and modeling and statistical physics. A multivariate Gaussian random number generator (MVGRNG) is one of the main building blocks of such a system. Field Programmable Gate Arrays (FPGAs) are gaining increased popularity as an alternative means to the traditional general purpose processors targeting the acceleration of the computationally expensive random number generator block due to their fine grain parallelism and reconfigurability properties and lower power consumption. As well as the ability to achieve hardware designs with high throughput it is also desirable to produce designs with the flexibility to control the resource usage in order to meet given resource constraints. This work proposes a novel approach for mapping a MVGRNG onto an FPGA by optimizing the computational path in terms of hardware resource usage subject to an acceptable error in the approximation of the distribution of interest. An analysis on the impact of the error due to truncation/rounding operation along the computational path is performed and an analytical expression of the error inserted into the system is presented. Extra dimensionality is added to the feature of the proposed algorithm by introducing a novel methodology to map many multivariate Gaussian random number generators onto a single FPGA. The effective resource sharing techniques introduced in this thesis allows further reduction in hardware resource usage. The use of MVGNRG can be found in a wide range of application, especially in financial applications which involve many correlated assets. In this work it is demonstrated that the choice of the objective function employed for the hardware optimization of the MVRNG core has a considerable impact on the final performance of the application of interest. Two of the most important financial applications, Value-at-Risk estimation and option pricing are considered in this work

Enhancing Grid Reliability With Phasor Measurement Units

Over the last decades, great efforts and investments have been made to increase the integration level of renewable energy resources in power grids. The New York State has set the goal to achieve 70% renewable generations by 2030, and realize carbon neutrality by 2040 eventually. However, the increased level of uncertainty brought about by renewables makes it more challenging to maintain stable and robust power grid operation. In addition to renewable energy resources, the ever-increasing number of electric vehicles and active loads have further increased the uncertainties in power systems. All these factors challenge the way the power grids are operated, and thus ask for new solutions to maintain stable and reliable grids. To meet the emerging requirements, advanced metering infrastructures are being integrated into power grids that transform traditional grids into \u27\u27 smart grids . One example is the widely deployed phasor measurement units (PMUs), which enable generating time-synchronized measurements with high sampling frequency, and pave a new path to realize real-time monitoring and control in power grids. However,the massive data generated by PMUs raises the questions of how to efficiently utilize the obtained measurements to understand and control the present system. Additionally, to meet the communication requirements between the advanced meters, the connectivity of the cyber layer has become more sophisticated, and thus is exposed to more cyber-attacks than before. Therefore, to enhance the grid reliability with PMUs, robust and efficient grid monitoring and control methods are required. This dissertation focuses on three important aspects of improving grid reliability with PMUs: (1) power system event detection; (2) impact assessment regarding both steady-state and transient stability; and (3) impact mitigation. In this dissertation, a comprehensive introduction of PMUs in the wide-area monitoring system, and comparisons with the existing supervisory control and data acquisition (SCADA) systems are presented first. Next, a data-driven event detection method is developed for efficient event detection with PMU measurements. A text mining approach is utilized to extract event oscillation patterns and determine event types. To ensure the integrity of the received data, the developed detection method is further designed to identify the fake events, and thus is robust against cyber-threat. Once a real event is detected, it is critical to promptly understand the consequences of the event in both steady and dynamic states. Sometimes, a single system event, e.g., a transmission line fault, may cause subsequent failures that lead to a cascading failure in the grid. In the worst case, these failures can result in large-scale blackouts. To assess the risk of an event in steady state, a probabilistic cascading failure model is developed. With the real-time phasor measurements, the failure probability of each system component at a specific operating condition can be predicted. In terms of the dynamic state, a failure of a system component may cause generators to lose synchronism, which will damage the power plant and lead to a blackout. To predict the transient stability after an event, a predictive online transient stability assessment (TSA) tool is developed in this dissertation. With only one sample of the PMU voltage measurements, the status of the transient stability can be predicted within cycles. In addition to the impact detection and assessment, it is also critical to identify proper mitigations to alleviate the failures. In this dissertation, a data-driven model predictive control strategy is developed. As a parameter-based system model is vulnerable to topology errors, a data-driven model is developed to mimic the grid behavior. Rather than utilizing the system parameters to construct the grid model, the data-driven model only leverages the received phasor measurements to determine proper corrective actions. Furthermore, to be robust against cyber-attacks, a check-point protocol, where past stored trustworthy data can be used to amend the attacked data, is utilized. The overall objective of this dissertation is to efficiently utilize advanced PMUs to detect, assess, and mitigate system failure, and help improve grid reliability

Accelerated Parameter Estimation with DALEχ\chi

We consider methods for improving the estimation of constraints on a high-dimensional parameter space with a computationally expensive likelihood function. In such cases Markov chain Monte Carlo (MCMC) can take a long time to converge and concentrates on finding the maxima rather than the often-desired confidence contours for accurate error estimation. We employ DALE$\chi$ (Direct Analysis of Limits via the Exterior of $\chi^2$) for determining confidence contours by minimizing a cost function parametrized to incentivize points in parameter space which are both on the confidence limit and far from previously sampled points. We compare DALE$\chi$ to the nested sampling algorithm implemented in MultiNest on a toy likelihood function that is highly non-Gaussian and non-linear in the mapping between parameter values and $\chi^2$. We find that in high-dimensional cases DALE$\chi$ finds the same confidence limit as MultiNest using roughly an order of magnitude fewer evaluations of the likelihood function. DALE$\chi$ is open-source and available at https://github.com/danielsf/Dalex.git