A Constrained Optimization Approach to Dynamic State Estimation for Power Systems Including PMU and Missing Measurements.

In this brief, a hybrid filter algorithm is developed to deal with the state estimation (SE) problem for power systems by taking into account the impact from the phasor measurement units (PMUs). Our aim is to include PMU measurements when designing the dynamic state estimators for power systems with traditional measurements. Also, as data dropouts inevitably occur in the transmission channels of traditional measurements from the meters to the control center, the missing measurement phenomenon is also tackled in the state estimator design. In the framework of extended Kalman filter (EKF) algorithm, the PMU measurements are treated as inequality constraints on the states with the aid of the statistical criterion, and then the addressed SE problem becomes a constrained optimization one based on the probability-maximization method. The resulting constrained optimization problem is then solved using the particle swarm optimization algorithm together with the penalty function approach. The proposed algorithm is applied to estimate the states of the power systems with both traditional and PMU measurements in the presence of probabilistic data missing phenomenon. Extensive simulations are carried out on the IEEE 14-bus test system and it is shown that the proposed algorithm gives much improved estimation performances over the traditional EKF method.

Parallel Time Series Analysis and Income Inequality: A New Approach to Comparative Case Studies

This case study deals with the role of time series analysis in sociology, and its relationship with the wider literature and methodology of comparative case study research. Time series analysis is now well-represented in top-ranked sociology journals, often in the form of ‘pooled time series’ research designs. These studies typically pool multiple countries together into a pooled time series cross-section panel, in order to provide a larger sample for more robust and comprehensive analysis. This approach is well suited to exploring trans-national phenomena, and for elaborating useful macro-level theories specific to social structures, national policies, and long-term historical processes. It is less suited however, to understanding how these global social processes work in different countries. As such, the complexities of individual countries - which often display very different or contradictory dynamics than those suggested in pooled studies – are subsumed. Meanwhile, a robust literature on comparative case-based methods exists in the social sciences, where researchers focus on differences between cases, and the complex ways in which they co-evolve or diverge over time. A good example of this is the inequality literature, where although panel studies suggest a general trend of rising inequality driven by the weakening power of labour, marketisation of welfare, and the rising power of capital, some countries have still managed to remain resilient. This case study takes a closer look at what can be learned by applying the insights of case-based comparative research to the method of time series analysis. Taking international income inequality as its point of departure, it argues that we have much to learn about the viability of different combinations of policy options by examining how they work in different countries over time. By taking representative cases from different welfare systems (liberal, social democratic, corporatist, or antipodean), we can better sharpen our theories of how policies can be more specifically engineered to offset rising inequality. This involves a fundamental realignment of the strategy of time series analysis, grounding it instead in a qualitative appreciation of the historical context of cases, as a basis for comparing effects between different countries.