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.

A voltage-adjustable three-phase rectifier with constant power flow

An three phase adjustable output voltage rectifier with constant power flow based on waveform gap patching principle is resented. By patching the gapes in the phase currents in parallel way as well as the ripple of the output voltage in series way, it implements the constant power flow from the three-phase line to the DC output without using any line frequency (and its harmonics) energy storage components. Principally, by treating only 22.4% power of the needed power output, this rectifier can supply constant power flow with adjustable output voltages without bring about any harmonic interferences to the power utility and achieve unite power factor.

基于工程地质力学的岩土工程加固理论、技术与实践

In the engineering reinforcement of-rock and soil mass, engineers must consider how to obtain better reinforcing effect at the cost of less reinforcing expense, which, in fact, is the aim of reinforcement design. In order to accomplish the purpose, they require not only researching the material used to reinforce and its structure, but also taking into account of several important geological factors, such as the structure and property of rock and soil mass. How to improve the reinforcing effect according to engineering geomechanical principle at the respect of the reinforcement of engineering soil and rock mass is studied and discussed in this paper. The author studies the theory, technology and practice of geotechnical reinforcement based on engineering geomechanics, taking example for the soil treatment of Zhengzhou Airport, the effect analysis of reinforcement to the slope on the left bank of Wuqiangxi Hydropower Station and the reinforcing design of the No. 102 Landslide and unique sand-slide slope on the Sichuan-Tibet Highway. The paper is comprised of two parts for the convenience of discussion. In the first part, from the first chapter to the fifth chapter, trying to perform the relevant research and application at the viewpoint of soil mass engineering geomechanics, the author mainly discusses the study of reinforcing soft ground soil through dynamical consolidation and its application. Then, in the second part, from the sixth chapter to the eleventh chapter, the study of new technologies in the rock slope reinforcement and their application are discussed. The author finds that not only better reinforcing effect can be gained in the research where the principle and method of rock mass engineering geomechanics is adopted, but also new reinforcing technologies can be put forward. Zhengzhou Airport is an important one in central plains. It lies on Yellow River alluvial deposit and the structure of stratum is complex and heterogeneous. The area of airport is very large, which can result in differential settlement easily, damage of airport and aircraft accident, whereas, there are no similar experiences to dispose the foundation, so the foundation treatment become a principal problem. During the process of treatment, the method of dynamic compaction was adopted after compared with other methods using the theory of synthetic integration. Dynamic compaction is an important method to consolidate foundation, which was successfully used in the foundation of Zhengzhou Airport. For fill foundation, controlling the thickness of fill so as to make the foundation treatment can reach the design demand and optimum thickness of the fill is a difficult problem. Considering this problem, the author proposed a calculation method to evaluate the thickness of fill. The method can consider not only the self-settlement of fill but also the settlement of the ground surface under applied load so as to ensure the settlement occurred during the using period can satisfy the design demand. It is proved that the method is correct after using it to choose reasonable energy of dynamic compaction to treat foundation. At the same time, in order to examine the effect of dynamic compaction, many monitor methods were adopted in the test such as static loading test, modulus of resilience test, deep pore pressure -test, static cone penetration test and the variation of the pore volume measurement. Through the tests, the author summarized the discipline of the accumulation and dissipation of pore pressure in Yellow River alluvial deposit under the action of dynamic compaction, gave a correct division of the property change of silt and clay under dynamic compaction, determined the bearing capacity of foundation after treatment and weighted the reinforcing effect of dynamic consolidation from the variation of the soil particle in microcosmic and the parameter of soil mass' density. It can be considered that the compactness of soil is in proportion to the energy of dynamic compaction. This conclusion provided a reference to the research of the "Problem of Soil Structure-the Central Problem of Soil Mechanics in 21 Century ". It is also important to strengthen rock mass for water conservancy and electric power engineering. Slip-resistance pile and anchoring adit full of reinforced concrete are usually adopted in engineering experience to strengthen rock mass and very important for engineering. But there also some deficiency such as the weakest section can't be highlighted, the monitor is inconvenient and the diameter of pile and adit is very large etc. The author and his supervisor professor Yangzhifa invented prestressed slip-resistance pile and prestressed anchoring adit full of reinforced concrete, utilizing the advantage that the prestressed structure has better anti-tensile characteristic (this invention is to be published). These inventions overcome the disadvantages of general slip-resistance pile and anchoring adit full of reinforced concrete and have the functions of engineering prospecting, strengthening, drainage and monitor simultaneous, so they have better strengthened effect and be more convenient for monitor and more economical than traditional methods. Drainage is an important factor in treatments of rock mass and slop. In view of the traditional drainage method that drainage pore often be clogged so as to resulted in incident, professor Yangzhifa invented the method and setting of guide penetration by fiber bundle. It would take good effect to use it in prestressed slip-resistance pile and anchoring adit full of reinforced concrete. In this paper, the author took example for anchoring adit full of reinforced concrete used to strengthen Wuqiangxi left bank to simulate the strengthened effect after consolidated by prestressed slip-resistance pile, took example for 102 landslide occurred along Sichuan-Tibet highway to simulate the application of slip-resistance pile and the new technology of drainage. At the same time the author proposed the treatment method of flowing sand in Sichuan-Tibet highway, which will benefit the study on strengthening similar engineering. There are five novelties in the paper with the author's theoretical study and engineering practice: 1. Summarizing the role of pore water pressure accumulation and dissipation of the Yellow River alluvial and diluvial soil under the action of dynamical consolidation, which has instructive significance in the engineering construction under the analogical engineering geological conditions in the future. It has not been researched by the predecessors. 2. Putting forward the concept of density D in microcosmic based on the microcosmical structure study of the soil sample. Adopting D to weight the reinforcing effect of dynamic consolidation is considered to be appropriate by the means of comparing the D values of Zhengzhou Airport's ground soil before with after dynamically consolidating reinforcement, so a more convenient balancing method can be provided for engineering practice. 3. According to the deep research into the soil mass engineering geology, engineering rock and soil science, soil mechanics, as well as considerable field experiments, improving the consolidating method in airport construction, from the conventional method, which is dynamically compactmg original ground surface firstly, then filling soil and dynamically layer-consolidating or layer-compacting at last to the upgraded method, which is performing dynamical consolidation after filling soil to place totally at the extent of the certain earth-filling depth. The result of the dynamical consolidation not only complies with the specifications, but also reduces the soil treatment investment by 10 million RMB. 4. Proposing the method for calculating the height of the filled soil by the means of estimating the potential displacement produced in the original ground surface and the filled earth soil under the possible load, selecting the appropriate dynamically-compacting power and determining the virtual height of the filled earth soil. The method is proved to be effective and scientific. 5. According to the thought of Engineering Geomechanics Metal-Synthetic Methodology (EGMS), patenting two inventions (to the stage of roclamation, with Professor Yang Zhi-fa, the cooperative tutor, and etc.) in which multi-functions, engineering geological investigation, reinforcement, drainage and strength remedy, are integrated all over in one body at the viewpoint of the breakage mechanism of the rock slope.

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.

Multi-Objective Reactive Power Support from Wind farms for Network Performance Enhancement

This paper examines the ability of the doubly fed induction generator (DFIG) to deliver multiple reactive power objectives during variable wind conditions. The reactive power requirement is decomposed based on various control objectives (e.g. power factor control, voltage control, loss minimisation, and flicker mitigation) defined around different time frames (i.e. seconds, minutes, and hourly), and the control reference is generated by aggregating the individual reactive power requirement for each control strategy. A novel coordinated controller is implemented for the rotor-side converter and the grid-side converter considering their capability curves and illustrating that it can effectively utilise the aggregated DFIG reactive power capability for system performance enhancement. The performance of the multi-objective strategy is examined for a range of wind and network conditions, and it is shown that for the majority of the scenarios, more than 92% of the main control objective can be achieved while introducing the integrated flicker control scheme with the main reactive power control scheme. Therefore, optimal control coordination across the different control strategies can maximise the availability of ancillary services from DFIG-based wind farms without additional dynamic reactive power devices being installed in power networks.

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.