Optimization and Control of Power Flow in Distribution Networks

Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators.

Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory.

The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.

High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Hatching date, nursery grounds, and early growth of juvenile walleye pollock (Theragra chalcogramma) off northern Japan*

Walleye pollock (Theragra chalcogramma) is widely distributed in the North Pacific Ocean and plays an important role in coastal subarctic ecosystems. The Japanese Pacific population of this species is one of the most important demersal fishes for commercial fisheries in northern Japan. The population is distributed along the Pacific coast of Hokkaido and the Tohoku area (Fig. 1), which is the southern limit of distribution of the species in the western North Pacific. In Funka Bay, the main spawning ground for this population, pollock spawn from December to March (Kendall and Nakatani, 1992). Planktonic eggs and larvae are transported into the bay, where juveniles usually remain until late July when they reach 60−85 mm in total length (Hayashi et al., 1968; Nakatani and Maeda, 1987). These juvenile pollock then migrate from Funka Bay eastward to the Doto area off southeastern Hokkaido (Honda et al., 2004). Many studies on eggs, larvae, and juveniles of the species have been conducted in or near Funka Bay, but little information is available on the ecology of the early life stages in the Tohoku area. Hashimoto and Ishito (1991) suggested that eggs are transported from Funka Bay southward to the Tohoku area by the coastal branch of the Oyashio Current, but there has been no study to verify this hypothesis.

A Biogeographic assessment off North/Central California: In support of the National Marine Sanctuaries of Cordell Bank, Gulf of the Farallones and Monterey Bay. Phase II - Environmental setting and update to marine birds and animals

NOAA’s National Centers for Coastal Ocean Science (NCCOS) conducts and supports research, monitoring, assessments, and technical assistance to meet NOAA’s coastal stewardship and management responsibilities. In 2001 the Biogeography Branch of NCCOS partnered with NOAA’s National Marine Sanctuary Program (NMSP) to conduct biogeographic assessments to support the management plan updates for the sanctuaries. The first biogeographic assessment conducted in this partnership focused on three sanctuaries off north/ central California: Cordell Bank, Gulf of the Farallones and Monterey Bay. Phase I of this assessment was conducted from 2001 to 2004, with the primary goal to identify and gather the best available data and information to characterize and identify important biological areas and time periods within the study area. The study area encompasses the three sanctuaries and extends along the coastal ocean off California from Pt. Arena to Pt. Sal (35°-39°N). This partnership project was lead by the NCCOS Biogeography Branch, but included over 90 contributors and 25 collaborating institutions. Phase I results include: 1) a report on the overall assessment that includes hundreds of maps, tables and analyses; 2) an ecological linkage report on the marine and estuarine ecosystems along the coast of north/central California, and 3) related geographic information system (GIS) data and other summary data files, which are available for viewing and download in several formats at the following website: http://ccma.nos.noaa.gov/products/biogeography/canms_cd/welcome.html Phase II (this report) was initiated in the Fall of 2004 to complete the analyses of marine mammals and update the marine bird colony information. Phase II resulted in significant updates to the bird and mammal chapters, as well as adding an environmental settings chapter, which contains new and existing data and maps on the study area. Specifically, the following Phase II topics and items were either revised or developed new for Phase II: •environmental, ecological settings – new maps on marine physiographic features, sea surface temperature and fronts, chlorophyll and productivity •all bird colony or roost maps, including a summary of marine bird colonies •updated at-sea data CDAS data set (1980-2003) •all mammal maps and descriptions •new overall density maps for eight mammal species •new summary pinniped rookery/haulout map •new maps on at-sea richness for cetaceans and pinnipeds •most text in the mammal chapter •new summary tables for mammals on population status and spatial and temporal patterns

Survey and impact assessment of derelict fish traps in St. Thomas and St. John, U.S. Virgin Islands

Since 2001, NOAA National Centers for Coastal Ocean Science (NCCOS), Center for Coastal Monitoring and Assessment’s (CCMA) Biogeography Branch (BB) has been working with federal and territorial partners to characterize, monitor, and assess the status of the marine environment across the U.S. Virgin Islands (USVI). At the request of the St. Thomas Fisherman’s Association (STFA) and NOAA Marine Debris Program, CCMA BB developed new partnerships and novel technologies to scientifically assess the threat from derelict fish traps (DFTs). Traps are the predominant gear used for finfish and lobster harvesting in St. Thomas and St. John. Natural phenomena (ground swells, hurricanes) and increasing competition for space by numerous user groups have generated concern about increasing trap loss and the possible ecological, as well as economic, ramifications. Prior to this study, there was a general lack of knowledge regarding derelict fish traps in the Caribbean. No spatially explicit information existed regarding fishing effort, abundance and distribution of derelict traps, the rate at which active traps become derelict, or areas that are prone to dereliction. Furthermore, there was only limited information regarding the impacts of derelict traps on natural resources including ghost fishing. This research identified two groups of fishing communities in the region: commercial fishing that is most active in deeper waters (30 m and greater) and an unknown number of unlicensed subsistence and or commercial fishers that fish closer to shore in shallower waters (30 m and less). In the commercial fishery there are an estimated 6,500 active traps (fish and lobster combined). Of those traps, nearly 8% (514) were reported lost during the 2008-2010 period. Causes of loss/dereliction include: movement of the traps or loss of trap markers due to entanglement of lines by passing vessels; theft; severe weather events (storms, large ground swells); intentional disposal by fishermen; traps becoming caught on various bottom structures (natural substrates, wrecks, etc.); and human error.

Coral reef ecosystems of St. John, U.S. Virgin Islands: spatial and temporal patterns in fish and benthic communities (2001-2009)

Scientific and anecdotal observations during recent decades have suggested that the structure and function of the coral reef ecosystems around St. John, U.S. Virgin Islands have been impacted adversely by a wide range of environmental stressors. Major stressors included the mass die-off of the long-spined sea urchin (Diadema antillarum) in the early 1980s, a series of hurricanes (David and Frederick in 1979, and Hugo in 1989), overfishing, mass mortality of Acropora species and other reef-building corals due to disease and several coral bleaching events. In response to these adverse impacts, the National Centers for Coastal Ocean Science (NCCOS), Center for Coastal Monitoring and Assessment, Biogeography Branch (CCMA-BB) collaborated with federal and territorial partners to characterize, monitor, and assess the status of the marine environment around the island from 2001 to 2012. This 13-year monitoring effort, known as the Caribbean Coral Reef Ecosystem Monitoring Project (CREM), was supported by the NOAA Coral Reef Conservation Program as part of their National Coral Reef Ecosystem Monitoring Program. This technical memorandum contains analysis of nine years of data (2001-2009) from in situ fish belt transect and benthic habitat quadrat surveys conducted in and around the Virgin Islands National Park (VIIS) and the Virgin Islands Coral Reef National Monument (VICR). The purpose of this document is to: 1) Quantify spatial patterns and temporal trends in (i) benthic habitat composition and (ii) fish species abundance, size structure, biomass, and diversity; 2) Provide maps showing the locations of biological surveys and broad-scale distributions of key fish and benthic species and assemblages; and 3) Compare benthic habitat composition and reef fish assemblages in areas under NPS jurisdiction with those in similar areas not managed by NPS (i.e., outside of the VIIS and VICR boundaries). This report provides key information to help the St. John management community and others understand the impacts of natural and man-made perturbations on coral reef and near-shore ecosystems. It also supports ecosystem-based management efforts to conserve the region’s coral reef and related fauna while maintaining the many goods and ecological services that they offer to society.

Benthic habitats of Fish Bay, Coral Bay and the St. Thomas East End Reserve

NOAA’s National Centers for Coastal Ocean Science Biogeography Branch has mapped and characterized large portions of the coral reef ecosystems inside the U.S. coastal and territorial waters, including the U.S. Caribbean. The complementary protocols used in these efforts have enabled scientists and managers to quantitatively and qualitatively compare marine ecosystems in tropical U.S. waters. The Biogeography Branch used similar protocols to generate new benthic habitat maps for Fish Bay, Coral Bay and the St. Thomas East End Reserve (STEER). While this mapping effort marks the third time that some of these shallow-water habitats (≤40 m) have been mapped, it is the first time that nearly 100% of the seafloor has been characterized in each of these areas. It is also the first time that high resolution imagery describing seafloor depth has been collected in each of these areas. Consequently, these datasets provide new information describing the distribution of coral reef ecosystems and serve as a spatial baseline for monitoring change in the Fish Bay, Coral Bay and the STEER. Benthic habitat maps were developed for approximately 64.3 square kilometers of seafloor in and around Fish Bay, Coral Bay and the STEER. Twenty seven percent (17.5 square kilometers) of these habitat maps describe the seafloor inside the boundaries of the STEER, the Virgin Islands National Park and the Virgin Islands Coral Reef National Monument. The remaining 73% (46.8 square kilometers) describe the seafloor outside of these MPA boundaries. These habitat maps were developed using a combination of semi-automated and manual classification methods. Habitats were interpreted from aerial photographs and LiDAR (Light Detection and Ranging) imagery. In total, 155 distinct combinations of habitat classes describing the geology and biology of the seafloor were identified from the source imagery.

Fish movement patterns in Virgin Islands National Park, Virgin Islands Coral Reef National Monument and adjacent waters

NOAA’s National Centers for Coastal Ocean Science (NCCOS)-Center for Coastal Monitoring and Assessment’s (CCMA) Biogeography Branch, National Park Service (NPS), US Geological Survey, and the University of Hawaii used acoustic telemetry to quantify spatial patterns and habitat affinities of reef fishes around the island of St. John, US Virgin Islands. The objective of the study was to define the movements of reef fishes among habitats within and between the Virgin Islands Coral Reef National Monument (VICRNM), the Virgin Islands National Park (VIIS), and Territorial waters surrounding St. John. In order to better understand species’ habitat utilization patterns among management regimes, we deployed an array of hydroacoustic receivers and acoustically tagged reef fishes. Thirty six receivers were deployed in shallow near-shore bays and across the shelf to depths of approximately 30 m. One hundred eighty four individual fishes were tagged representing 19 species from 10 different families with VEMCO V9-2L-R64K transmitters. The array provides fish movement information at fine (e.g., day-night and 100s meters within a bay) to broad spatial and temporal scales (multiple years and 1000s meters across the shelf). The long term multi-year tracking project provides direct evidence of connectivity across habitat types in the seascape and among management units. An important finding for management was that a number of individuals moved among management units (VICRNM, VINP, Territorial waters) and several snapper moved from near-shore protected areas to offshore shelf-edge spawning aggregations. However, most individuals spent the majority of their time with VIIS and VICRNM, with only a few wide-ranging species moving outside the management units. Five species of snappers (Lutjanidae) accounted for 31% of all individuals tagged, followed by three species of grunts (Haemulidae) accounting for an additional 23% of the total. No other family had more than a single species represented in the study. Bluestripe grunt (Haemulon sciurus) comprised 22% of all individuals tagged, followed by lane snappers (Lutjanus synagris) at 21%, bar jack (Carangoides ruber) at 11%, and saucereye porgy (Calamus calamus) at 10%. The largest individual tagged was a 70 cm TL nurse shark (Ginglymostoma cirratum), followed by a 65 cm mutton snapper (Lutjanus analis), a 47 cm bar jack, and a 41 cm dog snapper (Lutjanus jocu). The smallest individuals tagged were a 19 cm blue tang (Acanthurus coeruleus) and a 19.2 cm doctorfish (Acanthurus chirurgus). Of the 40 bluestriped grunt acoustically tagged, 73% were detected on the receiver array. The average days at large (DAL) was 249 (just over 8 months), with one individual detected for 930 days (over two and a half years). Lane snapper were the next most abundant species tagged (N = 38) with 89% detected on the array. The average days at large (DAL) was 221 with one individual detected for 351 days. Seventy-one percent of the bar jacks (N = 21) were detected on the array with the average DALs at 47 days. All of the mutton snapper (N = 12) were detected on the array with an average DAL of 273 and the longest at 784. The average maximum distance travelled (MDT) was ca. 2 km with large variations among species. Grunts, snappers, jacks, and porgies showed the greatest movements. Among all individuals across species, there was a positive and significant correlation between size of individuals and MDT and between DAL and MDT.

Integration of fisheries acoustics surveys and bathymetric mapping to characterize midwater-seafloor habitats of US Virgin Islands and Puerto Rico (2008-2010)

NOAA’s Coral Reef Conservation program (CRCP) develops coral reef management priorities by bringing together various partners to better understand threats to coral reef ecosystems with the goal of conserving, protecting and restoring these resources. Place-based and ecosystem-based management approaches employed by CRCP require that spatially explicit information about benthic habitats and fish utilization are available to characterize coral reef ecosystems and set conservation priorities. To accomplish this, seafloor habitat mapping of coral reefs around the U.S. Virgin Islands (USVI) and Puerto Rico has been ongoing since 2004. In 2008, fishery acoustics surveys were added to NOAA survey missions in the USVI and Puerto Rico to assess fish distribution and abundance in relation to benthic habitats in high priority conservation areas. NOAA’s National Centers for Coastal Ocean Science (NCCOS) have developed fisheries acoustics survey capabilities onboard the NOAA ship Nancy Foster to complement the CRCP seafloor habitat mapping effort spearheaded by the Center for Coastal Monitoring and Assessment Biogeography Branch (CCMA-BB). The integration of these activities has evolved on the Nancy Foster over the three years summarized in this report. A strategy for improved operations and products has emerged over that time. Not only has the concurrent operation of multibeam and fisheries acoustics surveys been beneficial in terms of optimizing ship time and resources, this joint effort has advanced an integrated approach to characterizing bottom and mid-water habitats and the fishes associated with them. CCMA conducts multibeam surveys to systematically map and characterize coral reef ecosystems, resulting in products such as high resolution bathymetric maps, backscatter information, and benthic habitat classification maps. These products focus on benthic features and live bottom habitats associated with them. NCCOS Centers (the Center for Coastal Fisheries and Habitat Research and the Center for Coastal Environmental Health and Biomolecular Research) characterize coral reef ecosystems by using fisheries acoustics methods to capture biological information through the entire water column. Spatially-explicit information on marine resources derived from fisheries acoustics surveys, such as maps of fish density, supports marine spatial planning strategies and decision making by providing a biological metric for evaluating coral reef ecosystems and assessing impacts from pollution, fishing pressure, and climate change. Data from fisheries acoustics surveys address management needs by providing a measure of biomass in management areas, detecting spatial and temporal responses in distribution relative to natural and anthropogenic impacts, and identifying hotspots that support high fish abundance or fish aggregations. Fisheries acoustics surveys conducted alongside multibeam mapping efforts inherently couple water column data with information on benthic habitats and provide information on the heterogeneity of both benthic habitats and biota in the water column. Building on this information serves to inform resource managers regarding how fishes are organized around habitat structure and the scale at which these relationships are important. Where resource managers require place-based assessments regarding the location of critical habitats along with high abundances of fish, concurrent multibeam and fisheries acoustics surveys serve as an important tool for characterizing and prioritizing coral reef ecosystems. This report summarizes the evolution of fisheries acoustics surveys onboard the NOAA ship Nancy Foster from 2008 to 2010, in conjunction with multibeam data collection, aimed at characterizing benthic and mid-water habitats in high priority conservation areas around the USVI and Puerto Rico. It also serves as a resource for the continued development of consistent data products derived from acoustic surveys. By focusing on the activities of 2010, this report highlights the progress made to date and illustrates the potential application of fisheries data derived from acoustic surveys to the management of coral reef ecosystems.

The coupling of St. John, US Virgin Islands Marine Protected Areas based on reef fish habitat affinities and movements across management boundaries [Poster]

NOAA's Biogeograpy Branch, the National Park Service (NPS), US Geological Survey, and the University of the Virgin Islands (UVI) are using acoustice telemetry to quantify spatial patterns and habitat affinities of reef fishes in the US Virgin Islands (USVI). The objective of the study is to define the movements of reef fishes among habitats within and between the Virgin Islands Coral Reef Nationla Monument (VICRNM), adjacent to Virgin Islands National Park (VIIS), and USVI Territorial waters. In order to better understand species habitat utilization patterns and movement of fishes among management regimes and areas open to fishing around St. John, we deployed an array of hydroacoutstic receivers and acoustically tagged reef fishes. A total of 150 fishes, representing 18 species and 10 families were acoustically tagged along the south shore of St. John from July 2006 to June 2008. Thirty six receivers with a detection range of approximately 300m each were deployed in shallow nearshore bays and across the shelf to depths of approximately 30m. Receivers were located within reefs and adjacent to reefs in seagrass, algal beds, or sand habitats. Example results include the movement of lane snappers and blue striped grunts that demonstrated diel movement from reef habitats during daytime hours to offshore seagrass beds at night. Fish associated with reefs that did not have adjacent seagrass beds made more extensive movements than those fishes associated with reefs that had adjacent seagrass habitats. The array comprised of both nearshore and cross shelf location of receives provides information on fine to broad scale fish movement patterns across habitats and among management units to examine the strength of ecological connectivity between management areas and habitats. For more information go to: http://ccma.nos.noaa.gov/ecosystems/ coralreef/acoustic_tracking.html