Phase Coherence Index, HHT and Wavelet Analysis to Extract Features from Active and Passive Distribution Networks  
[PERSON]  
1 Department of Electrical and Information Engineering, Polytechnic University of Bari, St. E. Orabona 4, 1-70125 Bari, Italy; [EMAIL_ADDRESS]. 1 Correspondence: [EMAIL_ADDRESS]; Tel. : +39-080-5963590; Fax: +39-080-59634101  
In this framework, the planning and the operation of the PDS under the SG paradigm are not trivial [15]; in fact, the several issues show different criticalities, whose solutions require different approaches. Two issues are the Optimal Operation of Smart Distribution Networks (OOSDN) [16] and the Load Forecasting (LF) [17]. OOSDN plays a key role for the sufficient power delivery to consumers, the integration of RES, and the economic energy management. The operation of power distribution systems can be divided into _real-time_ operation, when actions and commands occur in short time periods and are based on communication signals and state-estimation algorithms, and scheduled operation, when one day (or more days) ahead schedule is planned based on the demand and renewable power generation forecasting. Instead, LF techniques are used to predict future energy requirements of a system based on previous data, weather conditions, and availability of RES, ensuring the balance between demand and supply of energy. LF is mostly used for the prediction of future load on a given system for a specific period of time. In fact, LF can be classified into three main areas: (a) short term LF, used to predict load on hourly basis up to one week for daily running and cost minimization; (b) medium term LF that usually predicts load on weekly, monthly, and yearly basis for efficient operational planning; (c) long term LF, used to predict load up 50 years ahead to facilitate the expansion planning [17]. With this in mind, it is evident that the mathematical tools that are usually employed to extract features of short-time phenomena or devoted to the real-time operation are different from the ones utilized to study the medium term phenomena. For example, Refs. [18; 19] propose approaches to study the power quality of PDS, thus devoted to analyze short time phenomena. Other tools to study the short-time electrical behavior of the PDS are based on the Phasor Measurement Unit (PMU), which is an instrument that is able to measure amplitude, phase, frequency, and Rate of Change of Frequency (ROCOF) of voltage and current waveforms. PMUs are largely used at the transmission level of the power systems for protection purposes, while today, they are also utilized at the distribution level for several applications [20], because of the known issues that are related to the injection of PV power into the grid. Instead, other mathematical tools are employed to study the medium-term issues of PDS. Examples are [21; 22] for the forecasting, ref. [23] for the reliability, ref. [24] for the interaction with several RES, and so on. In particular, Wavelet Analysis (WA) is often utilized in this research area to detect and classify faults [25], to load forecast [26], and to monitor the PMU [27]. In [28], WA is utilized also in conjunction with the Empirical Mode Decomposition (EMD)--deriving from the Hilbert-Huang Transform (HHT)--to classify the power quality disturbances, while EMD is also integrated with artificial neural networks in [29] to forecast the short-term wind/speed of wind generators in large farm. Therefore, it is evident the importance to extract features by the electrical signals of power distribution systems, in order to prevent the failures, to attenuate the disturbances, to foresee the loads, and so on. For example, a time-frequency analysis for feature extraction is proposed in [30] with the aim to detect high-impedance faults, after having highlighted that the methods devoted to stationary signals return insufficient information, if they are applied to nonstationary and nonlinear signals.