Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

Fast response static var generator for improving the power system performance of an electric arc furnace (EAF)

Cascaded multilevel inverters-based Static Var Generators (SVGs) are FACTS equipment introduced for active and reactive power flow control. They eliminate the need for zigzag transformers and give a fast response. However, with regard to their application for flicker reduction in using Electric Arc Furnace (EAF), the existing multilevel inverter-based SVGs suffer from the following disadvantages. (1) To control the reactive power, an off-line calculation of Modulation Index (MI) is required to adjust the SVG output voltage. This slows down the transient response to the changes of reactive power; and (2) Random active power exchange may cause unbalance to the voltage of the d.c. link (HBI) capacitor when the reactive power control is done by adjusting the power angle d alone. To resolve these problems, a mathematical model of 11-level cascaded SVG, was developed. A new control strategy involving both MI (modulation index) and power angle (d) is proposed. A selected harmonics elimination method (SHEM) is taken for switching pattern calculations. To shorten the response time and simplify the controls system, feed forward neural networks are used for on-line computation of the switching patterns instead of using look-up tables. The proposed controller updates the MI and switching patterns once each line-cycle according to the sampled reactive power Qs. Meanwhile, the remainder reactive power (compensated by the MI) and the reactive power variations during the line-cycle will be continuously compensated by adjusting the power angles, d. The scheme senses both variables MI and d, and takes action through the inverter switching angle, qi. As a result, the proposed SVG is expected to give a faster and more accurate response than present designs allow. In support of the proposal there is a mathematical model for reactive powered distribution and a sensitivity matrix for voltage regulation assessment, MATLAB simulation results are provided to validate the proposed schemes. The performance with non-linear time varying loads is analysed and refers to a general review of flicker, of methods for measuring flickers due to arc furnace and means for mitigation.

Using SPICE for power system simulations

Power system simulation software is a useful tool for teaching the fundamentals of power system design and operation. However, existing commercial packages are not ideal for teaching work-based students because of high-cost, complexity of the software and licensing restrictions. This paper describes a set of power systems libraries that have been developed for use with the free, student-edition of a Micro-Cap Spice that overcomes these problems. In addition, these libraries are easily adapted to include power electronic converter based components into the simulation, such as HVDC, FACTS and smart-grid devices, as well as advanced system control functions. These types of technology are set to become more widespread throughout existing power networks, and their inclusion into a power engineering degree course is therefore becoming increasingly important.

A review of the effects of distributed energy resources and power-electronic controlled loading on distribution network stability

This paper looks at potential distribution network stability problems under the Smart Grid scenario. This is to consider distributed energy resources (DERs) e.g. renewable power generations and intelligent loads with power-electronic controlled converters. The background of this topic is introduced and potential problems are defined from conventional power system stability and power electronic system stability theories. Challenges are identified with possible solutions from steady-state limits, small-signal, and large-signal stability indexes and criteria. Parallel computation techniques might be included for simulation or simplification approaches are required for a largescale distribution network analysis.

Real-time temperature estimation for power MOSFETs considering thermal ageing effects

This paper presents a novel real-time power-device temperature estimation method that monitors the power MOSFET's junction temperature shift arising from thermal aging effects and incorporates the updated electrothermal models of power modules into digital controllers. Currently, the real-time estimator is emerging as an important tool for active control of device junction temperature as well as online health monitoring for power electronic systems, but its thermal model fails to address the device's ongoing degradation. Because of a mismatch of coefficients of thermal expansion between layers of power devices, repetitive thermal cycling will cause cracks, voids, and even delamination within the device components, particularly in the solder and thermal grease layers. Consequently, the thermal resistance of power devices will increase, making it possible to use thermal resistance (and junction temperature) as key indicators for condition monitoring and control purposes. In this paper, the predicted device temperature via threshold voltage measurements is compared with the real-time estimated ones, and the difference is attributed to the aging of the device. The thermal models in digital controllers are frequently updated to correct the shift caused by thermal aging effects. Experimental results on three power MOSFETs confirm that the proposed methodologies are effective to incorporate the thermal aging effects in the power-device temperature estimator with good accuracy. The developed adaptive technologies can be applied to other power devices such as IGBTs and SiC MOSFETs, and have significant economic implications.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Modelling of induction motors for system faults and transient stability studies

The research carried out in this thesis was mainly concerned with the effects of large induction motors and their transient performance in power systems. Computer packages using the three phase co-ordinate frame of reference were developed to simulate the induction motor transient performance. A technique using matrix algebra was developed to allow extension of the three phase co-ordinate method to analyse asymmetrical and symmetrical faults on both sides of the three phase delta-star transformer which is usually required when connecting large induction motors to the supply system. System simulation, applying these two techniques, was used to study the transient stability of a power system. The response of a typical system, loaded with a group of large induction motors, two three-phase delta-star transformers, a synchronous generator and an infinite system was analysed. The computer software developed to study this system has the advantage that different types of fault at different locations can be studied by simple changes in input data. The research also involved investigating the possibility of using different integrating routines such as Runge-Kutta-Gill, RungeKutta-Fehlberg and the Predictor-Corrector methods. The investigation enables the reduction of computation time, which is necessary when solving the induction motor equations expressed in terms of the three phase variables. The outcome of this investigation was utilised in analysing an introductory model (containing only minimal control action) of an isolated system having a significant induction motor load compared to the size of the generator energising the system.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

DC power line communication based on power/signal dual modulation in phase shift full bridge converters

For intelligent DC distributed power systems, data communication plays a vital role in system control and device monitoring. To achieve communication in a cost effective way, power/signal dual modulation (PSDM), a method that integrates data transmission with power conversion, can be utilized. In this paper, an improved PSDM method using phase shift full bridge (PSFB) converter is proposed. This method introduces a phase control based freedom in the conventional PSFB control loop to realize communication using the same power conversion circuit. In this way, decoupled data modulation and power conversion are realized without extra wiring and coupling units, and thus the system structure is simplified. More importantly, the signal intensity can be regulated by the proposed perturbation depth, and so this method can adapt to different operating conditions. Application of the proposed method to a DC distributed power system composed of several PSFB converters is discussed. A 2kW prototype system with an embedded 5kbps communication link has been implemented, and the effectiveness of the method is verified by experimental results.

A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Dynamic QoS management and optimisation in service-based systems

Service-based systems that are dynamically composed at run time to provide complex, adaptive functionality are currently one of the main development paradigms in software engineering. However, the Quality of Service (QoS) delivered by these systems remains an important concern, and needs to be managed in an equally adaptive and predictable way. To address this need, we introduce a novel, tool-supported framework for the development of adaptive service-based systems called QoSMOS (QoS Management and Optimisation of Service-based systems). QoSMOS can be used to develop service-based systems that achieve their QoS requirements through dynamically adapting to changes in the system state, environment and workload. QoSMOS service-based systems translate high-level QoS requirements specified by their administrators into probabilistic temporal logic formulae, which are then formally and automatically analysed to identify and enforce optimal system configurations. The QoSMOS self-adaptation mechanism can handle reliability- and performance-related QoS requirements, and can be integrated into newly developed solutions or legacy systems. The effectiveness and scalability of the approach are validated using simulations and a set of experiments based on an implementation of an adaptive service-based system for remote medical assistance.

Modelling and simulation strategies for the electric systems of large passenger aircraft

The simulation of a power system such as the More Electric Aircraft is a complex problem. There are conflicting requirements of the simulation, for example in order to reduce simulation run-times, power ratings that need to be established over long periods of the flight can be calculated using a fairly coarse model, whereas power quality is established over relatively short periods with a detailed model. An important issue is to establish the requirements of the simulation work at an early stage. This paper describes the modelling and simulation strategy adopted for the UK TIMES project, which is looking into the optimisation of the More Electric Aircraft from a system level. Essentially four main requirements of the simulation work have been identified, resulting in four different types of simulation. Each of the simulations is described along with preliminary models and results.

Credibility theory-based available transfer capability assessment

Since the development of large scale power grid interconnections and power markets, research on available transfer capability (ATC) has attracted great attention. The challenges for accurate assessment of ATC originate from the numerous uncertainties in electricity generation, transmission, distribution and utilization sectors. Power system uncertainties can be mainly described as two types: randomness and fuzziness. However, the traditional transmission reliability margin (TRM) approach only considers randomness. Based on credibility theory, this paper firstly built models of generators, transmission lines and loads according to their features of both randomness and fuzziness. Then a random fuzzy simulation is applied, along with a novel method proposed for ATC assessment, in which both randomness and fuzziness are considered. The bootstrap method and multi-core parallel computing technique are introduced to enhance the processing speed. By implementing simulation for the IEEE-30-bus system and a real-life system located in Northwest China, the viability of the models and the proposed method is verified.

PSD modifications of FHRV due to interpolation and CTG storage rate

Cardiotocographic data provide physicians information about foetal development and permit to assess conditions such as foetal distress. An incorrect evaluation of the foetal status can be of course very dangerous. To improve interpretation of cardiotocographic recordings, great interest has been dedicated to foetal heart rate variability spectral analysis. It is worth reminding, however, that foetal heart rate is intrinsically an uneven series, so in order to produce an evenly sampled series a zero-order, linear or cubic spline interpolation can be employed. This is not suitable for frequency analyses because interpolation introduces alterations in the foetal heart rate power spectrum. In particular, interpolation process can produce alterations of the power spectral density that, for example, affects the estimation of the sympatho-vagal balance (computed as low-frequency/high-frequency ratio), which represents an important clinical parameter. In order to estimate the frequency spectrum alterations of the foetal heart rate variability signal due to interpolation and cardiotocographic storage rates, in this work, we simulated uneven foetal heart rate series with set characteristics, their evenly spaced versions (with different orders of interpolation and storage rates) and computed the sympatho-vagal balance values by power spectral density. For power spectral density estimation, we chose the Lomb method, as suggested by other authors to study the uneven heart rate series in adults. Summarising, the obtained results show that the evaluation of SVB values on the evenly spaced FHR series provides its overestimation due to the interpolation process and to the storage rate. However, cubic spline interpolation produces more robust and accurate results. © 2010 Elsevier Ltd. All rights reserved.