Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Americium nuclear battery for space power applications

The work presents simplified242mAm fueled nuclear battery concept design featuring direct fission products energy conversion and passive heat rejection. The performed calculations of power conversion efficiency under thermal and nuclear design constraints showed that 14 W/kg power density can be achieved, which corresponds to conversion efficiency of about 6%. Total power of the battery scales linearly with its surface area. 144 kW of electric power can be produced by a nuclear battery with an external radius of about 174 cm and total mass of less than 10300 kg. The mass of242m Am fuel for such a system is 3200 gram.

Addressing non-linear hardware limitations and extending network coverage area for power aware wireless sensor networks

Science Foundation Ireland (07/CE/11147); Irish Research Council for Science Engineering and Technology (Embark Initiative)

Grid integration of wave energy & generic modelling of ocean devices for power system studies

The work presented in this thesis covers four major topics of research related to the grid integration of wave energy. More specifically, the grid impact of a wave farm on the power quality of its local network is investigated. Two estimation methods were developed regarding the flicker level Pst generated by a wave farm in relation to its rated power as well as in relation to the impedance angle ψk of the node in the grid to which it is connected. The electrical design of a typical wave farm design is also studied in terms of minimum rating for three types of costly pieces of equipment, namely the VAr compensator, the submarine cables and the overhead line. The power losses dissipated within the farm's electrical network are also evaluated. The feasibility of transforming a test site into a commercial site of greater rated power is investigated from the perspective of power quality and of cables and overhead line thermal loading. Finally, the generic modelling of ocean devices, referring here to both wave and tidal current devices, is investigated.

Low power predictable memory and processing architectures

Great demand in power optimized devices shows promising economic potential and draws lots of attention in industry and research area. Due to the continuously shrinking CMOS process, not only dynamic power but also static power has emerged as a big concern in power reduction. Other than power optimization, average-case power estimation is quite significant for power budget allocation but also challenging in terms of time and effort. In this thesis, we will introduce a methodology to support modular quantitative analysis in order to estimate average power of circuits, on the basis of two concepts named Random Bag Preserving and Linear Compositionality. It can shorten simulation time and sustain high accuracy, resulting in increasing the feasibility of power estimation of big systems. For power saving, firstly, we take advantages of the low power characteristic of adiabatic logic and asynchronous logic to achieve ultra-low dynamic and static power. We will propose two memory cells, which could run in adiabatic and non-adiabatic mode. About 90% dynamic power can be saved in adiabatic mode when compared to other up-to-date designs. About 90% leakage power is saved. Secondly, a novel logic, named Asynchronous Charge Sharing Logic (ACSL), will be introduced. The realization of completion detection is simplified considerably. Not just the power reduction improvement, ACSL brings another promising feature in average power estimation called data-independency where this characteristic would make power estimation effortless and be meaningful for modular quantitative average case analysis. Finally, a new asynchronous Arithmetic Logic Unit (ALU) with a ripple carry adder implemented using the logically reversible/bidirectional characteristic exhibiting ultra-low power dissipation with sub-threshold region operating point will be presented. The proposed adder is able to operate multi-functionally.

Power system parameters forecasting using Hilbert-Huang transform and machine learning

A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and a feature analysis of initial retrospective data using the Hilbert-Huang transform and machine learning algorithms. The random forests and gradient boosting trees learning techniques were examined. The decision tree techniques were used to rank the importance of variables employed in the forecasting models. The Mean Decrease Gini index is employed as an impurity function. The resulting hybrid forecasting models employ the radial basis function neural network and support vector regression. A part from introduction and references the paper is organized as follows. The second section presents the background and the review of several approaches for short-term forecasting of power system parameters. In the third section a hybrid machine learningbased algorithm using Hilbert-Huang transform is developed for short-term forecasting of power system parameters. Fourth section describes the decision tree learning algorithms used for the issue of variables importance. Finally in section six the experimental results in the following electric power problems are presented: active power flow forecasting, electricity price forecasting and for the wind speed and direction forecasting.

Voltage and power quality improvement strategy for a DFIG wind turbine during variable wind conditions

This paper presents a voltage and power quality enhancement scheme for a doubly-fed induction generator (DFIG) wind farm during variable wind conditions. The wind profiles were derived considering the measured data at a DFIG wind farm located in Northern Ireland (NI). The aggregated DFIG wind farm model was validated using measured data at a wind farm during variable generation. The voltage control strategy was developed considering the X/R ratio of the wind farm feeder which connects the wind farm and the grid. The performance of the proposed strategy was evaluated for different X/R ratios, and wind profiles with different characteristics. The impact of flicker propagation along the wind farm feeder and effectiveness of the proposed strategy is also evaluated with consumer loads connected to the wind farm feeder. It is shown that voltage variability and short-term flicker severity is significantly reduced following implementation of the novel strategy described.

An ultra-short-term wind power prediction method using “offline classification and optimization, online model matching” based on time series features

The applicability of ultra-short-term wind power prediction (USTWPP) models is reviewed. The USTWPP method proposed extracts featrues from historical data of wind power time series (WPTS), and classifies every short WPTS into one of several different subsets well defined by stationary patterns. All the WPTS that cannot match any one of the stationary patterns are sorted into the subset of nonstationary pattern. Every above WPTS subset needs a USTWPP model specially optimized for it offline. For on-line application, the pattern of the last short WPTS is recognized, then the corresponding prediction model is called for USTWPP. The validity of the proposed method is verified by simulations.

A novel radial basis function neural network principal component analysis scheme for PMU-based wide-area power system monitoring

A novel model-based principal component analysis (PCA) method is proposed in this paper for wide-area power system monitoring, aiming to tackle one of the critical drawbacks of the conventional PCA, i.e. the incapability to handle non-Gaussian distributed variables. It is a significant extension of the original PCA method which has already shown to outperform traditional methods like rate-of-change-of-frequency (ROCOF). The ROCOF method is quick for processing local information, but its threshold is difficult to determine and nuisance tripping may easily occur. The proposed model-based PCA method uses a radial basis function neural network (RBFNN) model to handle the nonlinearity in the data set to solve the no-Gaussian issue, before the PCA method is used for islanding detection. To build an effective RBFNN model, this paper first uses a fast input selection method to remove insignificant neural inputs. Next, a heuristic optimization technique namely Teaching-Learning-Based-Optimization (TLBO) is adopted to tune the nonlinear parameters in the RBF neurons to build the optimized model. The novel RBFNN based PCA monitoring scheme is then employed for wide-area monitoring using the residuals between the model outputs and the real PMU measurements. Experimental results confirm the efficiency and effectiveness of the proposed method in monitoring a suite of process variables with different distribution characteristics, showing that the proposed RBFNN PCA method is a reliable scheme as an effective extension to the linear PCA method.

An approach to determine the local boundary of small disturbance voltage stability region in a cut-set power space:基于微扰的割集电压稳定域局部边界求解方法

A new approach to determine the local boundary of voltage stability region in a cut-set power space (CVSR) is presented. Power flow tracing is first used to determine the generator-load pair most sensitive to each branch in the interface. The generator-load pairs are then used to realize accurate small disturbances by controlling the branch power flow in increasing and decreasing directions to obtain new equilibrium points around the initial equilibrium point. And, continuous power flow is used starting from such new points to get the corresponding critical points around the initial critical point on the CVSR boundary. Then a hyperplane cross the initial critical point can be calculated by solving a set of linear algebraic equations. Finally, the presented method is validated by some systems, including New England 39-bus system, IEEE 118-bus system, and EPRI-1000 bus system. It can be revealed that the method is computationally more efficient and has less approximation error. It provides a useful approach for power system online voltage stability monitoring and assessment. This work is supported by National Natural Science Foundation of China (No. 50707019), Special Fund of the National Basic Research Program of China (No. 2009CB219701), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200439), Tianjin Municipal Science and Technology Development Program (No. 09JCZDJC25000), National Major Project of Scientific and Technical Supporting Programs of China During the 11th Five-year Plan Period (No. 2006BAJ03A06). ©2009 State Grid Electric Power Research Institute Press.

A stochastic programming approach for the development of offering strategies for a wind power producer

A stochastic programming approach is proposed in this paper for the development of offering strategies for a wind power producer. The optimization model is characterized by making the analysis of several scenarios and treating simultaneously two kinds of uncertainty: wind power and electricity market prices. The approach developed allows evaluating alternative production and offers strategies to submit to the electricity market with the ultimate goal of maximizing profits. An innovative comparative study is provided, where the imbalances are treated differently. Also, an application to two new realistic case studies is presented. Finally, conclusions are duly drawn.

A Data Mining Framework for Electric Load Profiling

This paper consists in the characterization of medium voltage (MV) electric power consumers based on a data clustering approach. It is intended to identify typical load profiles by selecting the best partition of a power consumption database among a pool of data partitions produced by several clustering algorithms. The best partition is selected using several cluster validity indices. These methods are intended to be used in a smart grid environment to extract useful knowledge about customers’ behavior. The data-mining-based methodology presented throughout the paper consists in several steps, namely the pre-processing data phase, clustering algorithms application and the evaluation of the quality of the partitions. To validate our approach, a case study with a real database of 1.022 MV consumers was used.

Power to Gas - sähköenergiasta luonnonkaasua, liiketoimintamahdollisuudet Suomessa

Uusiutuvan sähköntuotannon osuuden kasvaessa kasvaa tarve tasata sähköntuotannon ja kulutuksen vaihteluita varastoimalla sähköä. Power to Gas (PtG) - sähköenergiasta luonnonkaasua tarjoaa yhden mahdollisuuden varastoida sähköä. Sähköä käytetään veden elektrolyysiin, jossa syntynyt vety käytetään metanoinissa yhdessä hiilidioksidin kanssa muodostamaan korvaavaa luonnonkaasua. Näin syntynyttä korvaava luonnonkaasua sähköstä kutsutaan e-SNG-kaasuksi. Tässä työssä tutkitaan PtG-laitoksen investointi, käyttö- ja kunnossapitokuluja. Työssä luodaan laskentamalli, jolla lasketaan PtG-laitoksen neljälle käyttötapaukselle kannattavuuslaskelma. Käyttötapauksille lasketaan myös herkkyystarkasteluja. Kannattavuuslaskelmien perusteella päätellään PtG-laitoksen liiketoimintamahdollisuudet Suomessa. Työssä laskettujen kannattavuuslaskelmien perusteella PtG-laitoksen perustapausten liiketoimintamahdollisuudet ovat huonot. Laskettujen herkkyystarkastelujen perusteella havaittiin, että investointikulut, laitoksen ajoaika ja lisätulot hapesta ja lämmöstä ovat kannattavuuden kannalta kriittisimmät menestystekijät.

Niagara-Welland Power Company Limited fonds, 1833, 1852, 1904-1906, 1909, n.d.

The Welland Power and Supply Canal Company Limited, established in 1893 and incorporated in 1894 with a capital stock of $500,000. The aim of the company was to harness the natural water supply of the Niagara and Welland Rivers. In 1898 the Canadian Electrical News published a report by Henry Symons, QC outlining the main project of the company. This project involves the construction of a canal from the Welland River to the brow of the mountain at Thorold, a distance of 8 miles; the construction at Thorold of a power house, and from Thorold to Lake Ontario, a raceway by which to carry water into the lake. The estimate for the machinery to generate 100,000 horse power is £125,000; for transmission line to Toronto at a voltage of 10,000….The total estimate therefore amounts to £2,452,162, or roughly speaking, $12,000,000. Source: Canadian Electrical News, August 1898, p. 172. In 1899 the company officers petitioned the federal government desiring a name change to the Niagara-Welland Power Company Limited. Officers of the company were Harry Symons, President; Charles A. Hesson, Vice-President; and M.R. O’Loughlin, James B. Sheehan, James S. Haydon, Frederick K. Foster, directors; John S. Campbell, secretary-treasurer. The company’s head offices were located in St. Catharines, with a New York (City) office on Broad Street. In 1905 and 1909 the company petitioned the federal government for additional time to construct its works, which was granted. The company had until May 16, 1915 to complete construction. John S. Campbell (1860-1950) was a graduate of the University of Toronto and Osgoode Hall. During his university years John began his military career first in "K" Company, Queens Own rifles and then later as Commanding Officer of the 19th Lincoln Regiment, from 1906 to 1910. Upon his return to St. Catharines John Campbell served as secretary in the St. Catharines Garrison Club, a social club for military men begun in 1899. After being called to the Bar, he became a partner in the firm of Campbell and McCarron and was appointed to the bench in 1916, serving until retirement in 1934. Judge Campbell served as an alderman for several terms and was the mayor of St. Catharines in 1908 and 1909. He also served as the first chairman of the St. Catharines Public Utilities in 1914. John S. Campbell was married to Elizabeth Oille, daughter of Jerome B. and Charlotte (St. John) Oille. The family home "Cruachan" was located at 32 Church St.