In the background of all human thinking—acting and reacting are sets of connections between different neurons or groups of neurons. We studied and evaluated these connections using electroencephalography (EEG) brain signals. In this paper, we propose the use of the complex Pearson correlation coefficient (CPCC), which provides information on connectivity with and without consideration of the volume conduction effect. Although the Pearson correlation coefficient is a widely accepted measure of the statistical relationships between random variables and the relationships between signals, it is not being used for EEG data analysis. Its meaning for EEG is not straightforward and rarely well understood. In this work, we compare it to the most commonly used undirected connectivity analysis methods, which are phase locking value (PLV) and weighted phase lag index (wPLI). First, the relationship between the measures is shown analytically. Then, it is illustrated by a practical comparison using synthetic and real EEG data. The relationships between the observed connectivity measures are described in terms of the correlation values between them, which are, for the absolute values of CPCC and PLV, not lower that 0.97, and for the imaginary component of CPCC and wPLI—not lower than 0.92, for all observed frequency bands. Results show that the CPCC includes information of both other measures balanced in a single complex-numbered index.

Contingency analysis (CA) is a well-known function in power system planning and operation. In accordance with CA results, the system operator dispenses information regarding static security of the power system (overloads and/or voltage outside tolerable limits). However, classic CA with remedial action schemes cannot distinguish safe operating regimes from potentially dangerous ones in terms of voltage (in)stability. In fact, voltage instability is considered as one of the major threats leading to power system insecurity. Therefore, in this study an enhanced contingency analysis (ECA) is presented where the classical CA is extended with static voltage analysis based on the modal analysis. The article presents a dedicated methodology for the proposed ECA tool, with special emphasis on the analysis of corrective measures provided by the system operator, intended for enhancing power system security (regulation transformer action, distributed generation and energy storage). Also the influence of the load model was analyzed by simulation and the main conclusions are presented. The study demonstrated the advantages that distributed generation resources and energy storage can provide in the context of voltage stability. Also, the simulations acknowledged the importance of correct load modeling, since over or under estimation of a certain load-type component can result in too optimistic or too pessimistic power system operation limits.

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Photovoltaic (PV) system inverters usually operate at unitary power factor, injecting only active power into the system. Recently, many studies have been done analyzing potential benefits of reactive power provisioning, such as voltage regulation, congestion mitigation and loss reduction. This article analyzes possibilities for loss reduction in a typical medium voltage distribution system. Losses in the system are compared to the losses in the PV inverters. Different load conditions and PV penetration levels are considered and for each scenario various active power generation by PV inverters are taken into account, together with allowable levels of reactive power provisioning. As far as loss reduction is considered, there is very small number of PV inverters operating conditions for which positive energy balance exists. For low and medium load levels, there is no practical possibility for loss reduction. For high loading levels and higher PV penetration specific reactive savings, due to reactive power provisioning, increase and become bigger than additional losses in PV inverters, but for a very limited range of power factors.

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