Statistical Inference for Large Spatial Data

The availability of large spatial and spatial-temporal data geocoded at accurate locations has fueled increasing interest in spatial modeling and analysis. In this dissertation, we present one study concerning the inference on properties of a single spatial process, and then turn to multiple processes and provide two modeling approaches exploring the spatially varying relationship between covariates and the response variable of interest. In the first study, we investigate the inference tool based on quasi-likelihood, composite likelihood (CL) method and propose a new weighting scheme to construct a CL for the inference of spatial Gaussian process models. This weight function approximates the optimal weight derived from the theory of estimating equations. It combines block-diagonal approximation and tapering strategy to facilitate computations. Gains in statistical and computational efficiency over existing CL methods are illustrated through simulation studies. The second investigation is the development of a new spatial modeling framework to capture the spatial structure, especially clustered structure in the relationship between response variable and explanatory variables. The proposed method, called Spatially Clustered Coefficient(SCC) regression, results in estimators of varying coefficients, which conveys important information about the changing pattern of the relationship. The SCC method works very effectively in estimation for data either with clustered coefficients or smoothly-varying coefficients, based on our simulation results. Thus, it allows the researchers to explore the spatial structure in the regression coefficient without any priori information. We also derive some oracle inequalities, which provides non-asymptotic error bounds on estimators and predictors. An application of the SCC method to temperature and salinity data in the Atlantic basin is provided for illustration. Motivated by the studies in Geoscience that the influence of turbulent heat flux on sea surface temperature (SST) varies at different spatial scales, we develop a statistical model to quantify the continuous dependence of SST-turbulent heat flux relationship (T-Q relationship) on spatial scales. In particular, we propose a penalized regression model in the spectral domain to estimate the changing relationship with spatial scales. While application to T-Q relationship is the main motivation for this work, it should be emphasized that the penalized spectral regression framework is general and thus is applicable to other phenomena of interest as well

Utility-Scale Estimation of Additional Reinforcement Cost from 3-Phase Imbalance Considering Thermal Constraints

Widespread three-phase imbalance causes inefficient uses of low voltage (LV) network assets, leading to additional reinforcement costs (ARCs). Previous work that assumed balanced three phases underestimated the reinforcement cost throughout the whole utility by more than 50%. Previous work that quantified the ARCs was limited to individual network components, relying on full sensory data. This paper proposes a novel methodology that will scale the ARC estimation at a utility level, when the data concerning the imbalance of circuits or transformers are scarce. A novel statistical method is developed to estimate the volume of assets that need to be invested by identifying the relationship between the triangular distribution of circuit imbalance and that of circuit utilization. When there are more data available in future, accurate probability distributions can be constructed to reflect the network condition across the whole system. In light of this, two novel generalized ARC estimation formulas are developed that account for generic probability distributions. The developed methodology is applied to a real utility system in the UK, showing that: 1) three-phase imbalance leads to ARCs that are even greater than the reinforcement costs in the balanced case; 2) a 1% increase in the demand growth rate, the maximum degree of imbalance (DIB) and the maximum nominal utilization rate leads to over 10%, approximately 1% and 2% increases in the ARCs, respectively; and 3) the ARC is not sensitive to the minimum DIB values and the minimum nominal utilization rates

Quantification of additional reinforcement cost driven by voltage constraint under three-phase imbalance

Three-phase imbalance causes uneven voltage drops across LV transformers and main feeders. With continuous load growth, the lowest phase voltage at the feeder end determines the voltage spare room, which is lower than if the same power were transmitted through balanced three phases. This imbalance causes additional reinforcement cost (ARC) beyond the balanced case. This paper proposes novel ARC models for a typical LV circuit based on primary-side voltage and current measurements. All models except the accurate model not only enable efficient utility-scale ARC calculations with sufficient accuracy but also remove the need for phasor measurements. The ARC models calculate voltage-driven reinforcement costs for the imbalanced case and the benchmark, i.e., the balanced case, where the ARC is the difference between the above values. The models include: an accurate ARC model considering imbalance in both magnitudes and phase angles; a semi-simplified ARC model assuming balanced phase angles; a fully simplified model assuming a purely resistive LV circuit and a unity power factor; and linearized ARC models considering the imbalance degree for two special cases. Test case proves that: the ARC is a monotonically increasing, convex (concave) but close-to-linear function of current (voltage) imbalance; voltage imbalance has a greater impact on ARCs than current imbalance; a higher degree of current imbalance and/or a deteriorating power factor reduce the accuracy of the fully simplified model; and the accuracy of the semi-simplified model is higher in the case of voltage angle imbalance than in the case of current angle imbalance

Regional nonintrusive load monitoring for low voltage substations and distributed energy resources

This paper presents a novel extension of the classic nonintrusive load monitoring (NILM) problem from household-appliance level to substation level. A new three-stage regional-NILM method is proposed to deduce the states of different types of loads in a region by disaggregating its substation demand. Three types of loads are considered in this study: (i) traditional loads; (ii) distributed generation such as photovoltaics (PVs); and (iii) flexible loads like electric vehicles (EVs). The proposed method firstly forecasts the traditional load using the long-term historical data and employing spectral analysis to boost the signal-to-noise ratio. Secondly, the PV capacity is deduced by performing peak coincidence analysis between negative residuals and local solar irradiance data. Finally, a novel limited activation matching pursuit method is proposed to estimate the states of the EVs, including the total EV load and number of EVs. The method is assessed on real data collected from 800 substations, 10 PVs and 50 EVs in the UK. Results show the proposed method for estimating the number of EVs outperforms the approaches based on sparse coding, orthogonal matching pursuit and non-negative matching pursuit by 16.5%, 10.2% and 10.0%, respectively. The proposed Regional-NILM solution provides a cost-effective way for distribution network operators to understand the network's state. It can therefore significantly increase the network visibility without requiring expensive monitoring and avoiding data privacy issues. As such, it can improve the efficiency of demand side management, which is required to accommodate the future large number of distributed energy resources connections.</p