Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.

Raman microscopy of formamide-intercalated kaolinites treated by controlled-rate thermal analysis technology

Raman spectroscopy of formamide-intercalated kaolinites treated using controlled-rate thermal analysis technology (CRTA), allowing the separation of adsorbed formamide from intercalated formamide in formamide-intercalated kaolinites, is reported. The Raman spectra of the CRTA-treated formamide-intercalated kaolinites are significantly different from those of the intercalated kaolinites, which display a combination of both intercalated and adsorbed formamide. An intense band is observed at 3629 cm-1, attributed to the inner surface hydroxyls hydrogen bonded to the formamide. Broad bands are observed at 3600 and 3639 cm-1, assigned to the inner surface hydroxyls, which are hydrogen bonded to the adsorbed water molecules. The hydroxyl-stretching band of the inner hydroxyl is observed at 3621 cm-1 in the Raman spectra of the CRTA-treated formamide-intercalated kaolinites. The results of thermal analysis show that the amount of intercalated formamide between the kaolinite layers is independent of the presence of water. Significant differences are observed in the CO stretching region between the adsorbed and intercalated formamide.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Determination of preventive maintenance lead time using hybrid analysis

The time for conducting Preventive Maintenance (PM) on an asset is often determined using a predefined alarm limit based on trends of a hazard function. In this paper, the authors propose using both hazard and reliability functions to improve the accuracy of the prediction particularly when the failure characteristic of the asset whole life is modelled using different failure distributions for the different stages of the life of the asset. The proposed method is validated using simulations and case studies.

Hydrazine-hydrate intercalated halloysite under controlled-rate thermal analysis conditions

The thermal behaviour of halloysite fully expanded with hydrazine-hydrate has been investigated in nitrogen atmosphere under dynamic heating and at a constant, pre-set decomposition rate of 0.15 mg min-1. Under controlled-rate thermal analysis (CRTA) conditions it was possible to resolve the closely overlapping decomposition stages and to distinguish between adsorbed and bonded reagent. Three types of bonded reagent could be identified. The loosely bonded reagent amounting to 0.20 mol hydrazine-hydrate per mol inner surface hydroxyl is connected to the internal and external surfaces of the expanded mineral and is present as a space filler between the sheets of the delaminated mineral. The strongly bonded (intercalated) hydrazine-hydrate is connected to the kaolinite inner surface OH groups by the formation of hydrogen bonds. Based on the thermoanalytical results two different types of bonded reagent could be distinguished in the complex. Type 1 reagent (approx. 0.06 mol hydrazine-hydrate/mol inner surface OH) is liberated between 77 and 103°C. Type 2 reagent is lost between 103 and 227°C, corresponding to a quantity of 0.36 mol hydrazine/mol inner surface OH. When heating the complex to 77°C under CRTA conditions a new reflection appears in the XRD pattern with a d-value of 9.6 Å, in addition to the 10.2 Ĺ reflection. This new reflection disappears in contact with moist air and the complex re-expands to the original d-value of 10.2 Å in a few h. The appearance of the 9.6 Å reflection is interpreted as the expansion of kaolinite with hydrazine alone, while the 10.2 Å one is due to expansion with hydrazine-hydrate. FTIR (DRIFT) spectroscopic results showed that the treated mineral after intercalation/deintercalation and heat treatment to 300°C is slightly more ordered than the original (untreated) clay.