On democracy

If one clear argument emerged from my doctoral thesis in political science, it is that there is no agreement as to what democracy is. There are over 40 different varieties of democracy ranging from those in the mainstream with subtle or minute differences to those playing by themselves in the corner. And many of these various types of democracy are very well argued, empirically supported, and highly relevant to certain polities. The irony is that the thing which all of these democratic varieties or the ‘basic democracy’ that all other forms of democracy stem from, is elusive. There is no international agreement in the literature or in political practice as to what ‘basic democracy’ is and that is problematic as many of us use the word ‘democracy’ every day and it is a concept of tremendous importance internationally. I am still uncertain as to why this problem has not been resolved before by far greater minds than my own, and it may have something to do with the recent growth in democratic theory this past decade and the innovative areas of thought my thesis required, but I think I’ve got the answer. By listing each type of democracy and filling the column next to this list with the literature associated with these various styles of democracy, I amassed a large and comprehensive body of textual data. My research intended to find out what these various styles of democracy had in common and to create a taxonomy (like the ‘tree of life’ in biology) of democracy to attempt at showing how various styles of democracy have ‘evolved’ over the past 5000 years.ii I then ran a word frequency analysis program or a piece of software that counts the 100 most commonly used words in the texts. This is where my logic came in as I had to make sense of these words. How did they answer what the most fundamental commonalities are between 40 different styles of democracy? I used a grounded theory analysis which required that I argue my way through these words to form a ‘theory’ or plausible explanation as to why these particular words and not others are the important ones for answering the question. It came down to the argument that all 40 styles of democracy analysed have the following in common 1) A concept of a citizenry. 2) A concept of sovereignty. 3) A concept of equality. 4) A concept of law. 5) A concept of communication. 6) And a concept of selecting officials. Thus, democracy is a defined citizenry with its own concept of sovereignty which it exercises through the institutions which support the citizenry’s understandings of equality, law, communication, and the selection of officials. Once any of these 6 concepts are defined in a particular way it creates a style of democracy. From this, we can also see that there can be more than one style of democracy active in a particular government as a citizenry is composed of many different aggregates with their own understandings of the six concepts.

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.