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There exist other possibilities of introducing correlation as compared to impulse response models of Chap. 5. We propose in this chapter an impulsive noise model using a Partitioned Markov Chain (PMC) in order to generate samples with a correlation that produces impulses with a damped oscillating waveform.

In several measurement campaigns in substations reported in Chap. 3, wideband impulsive noise waveforms emitted by partial discharges are transient, their samples are correlated and their power spectral densities have approximately a form of ∼ (f − f0)−γ, where f0 is the resonant frequency of the RF measurement setup and γ > 0 an arbitrary exponent.

In last chapters, an overview of electromagnetic interference induced by partial discharges and their impact on wireless communication systems has been discussed. Measurement campaigns in substations have been conducted. These sources can take place in high-voltage equipment like transformers, powerlines, bushing bars, etc.

This chapter gives a general overview of EMI and describes the measurement and characterization methods associated with them, in keeping with the latest research. Impulsive noise phenomenon in substations is particularly focused and existing impulsive noise models are discussed.

In Chaps. 4– 6 accurate impulsive noise models have been proposed. These can be used for performance analyses of robust wireless communication systems as well as the development of diagnostic tools in high voltage equipments. The development of rapid and online methods of detection, identification and/or localization of partial discharge (PD) sources using wireless intelligent electronic devices is an area of growing interest.

The phenomenon of impulsive noise is generated by Partial discharge (PD) sources in high-voltage substations. A PD generates a current impulse, acoustic noise, visible and ultraviolet (UV) light and electromagnetic radiation , and accordingly its presence can be detected via several measurement methods.

The installation of wireless technologies in power substations requires characterizing the impulsive noise produced by the high-voltage equipment. Substation impulsive noise might interfere with classic wireless communications and none of the existing models can reliably represent this noise in wide band. Previous studies have shown that impulsive noise is characterized by series of damped oscillations with the amplitude, the duration and the occurrence times of the impulses that are random. All these characteristics make this noise time-correlated and the partitioned Markov chain remains an efficient model that can ensure the correlation between the samples. In this study, we propose to design a partitioned Markov chain to generate an impulsive noise that is similar to the noise measured in existing substations, in time and frequency domains. We configure our Markov chain to produce the impulses with the damped oscillation effect, then, we determine the probability transition matrix and the distribution of each state of the Markov chain. Finally, we generate noise samples and we study the distribution of the impulsive noise characteristics. Our Markov chain model can replicate the correlation between the measured noise samples; also the distributions of the noise characteristics are similar in the simulations and the measurements.

Installing wireless Intelligent Electronic Devices (IED) for Substation Automation (SA) requires a thorough study of the electromagnetic radiations coming from the power equipment. In our previous work, we have performed a measurement campaign within several substations working under different voltages and we have recorded around 120 sequences of impulsive noise samples in the 700 MHz–2.5 GHz band. In this paper, we present a method to classify substation impulsive noise in order to characterize a representative Radio Frequency (RF) environment of substations for specific substation voltages. The main contribution of this work is to provide representative impulsive noise characteristics in order to calculate parameters for impulsive noise models and to improve the characterization of substation RF noise. To reach this objective, we classify impulsive noise characteristics, such as the impulse amplitude, the impulse duration and the repetition rate for substations under 25 kv, 230 kV, 315 kV and 735 kV. By using the impulsive noise characteristics, we estimate representative parameters for two impulsive noise models: the Middleton class-A (MCA) and the Bernoulli-Gaussian with memory (BGM).

Power substations generate a significant “bursty impulse noise” that might interfere with wireless technologies working in the vicinity of power equipment. Existing wireless systems are not designed for such an environment; we propose a Maximum a Posteriori (MAP) receiver designed with Markov-Gaussian models in order to mitigate the impact of impulsive noise in substations. We study and compare different noise models implemented in the receiver and we discuss the performance of the receiver based on the characteristics of the impulsive noise. Our proposed model can be used by a MAP receiver to offer optimum performances from low signal to noise ratio (SNR). When the communication is disturbed by impulsive noise measured in the field, the MAP receiver still offers better performance than when using other models, but mainly at higher SNR.

The partitioned Markov chain is a sample noise model that can represent impulsive noise in power substation including the time-correlation between the samples. In order to use this model, algorithms are needed to detect and to estimate the impulses characteristics, such as the duration, the samples values and the occurrence times of the impulses. Unsupervised learning of these characteristics is very complex, we propose then to use the fuzzy C-means algorithm to analyze impulses from substation measurements and to configure the partitioned Markov chain model by instantiating the transition matrix and by estimating the parameters of the Gaussian distributions associated with the Markov states. After simulating sequences of samples with our model, we noticed that the distribution of the impulsive noise characteristics and the power spectrum of the impulses are satisfyingly close to the measurements. The fuzzy C-means algorithm is appropriate to estimate the parameters required by the partitioned Markov chain model and to reduce the complexity of the parameter estimation.

Impulsive noise in air-insulated substations is created by partial discharges, Corona and gap noises. In order to install a wireless sensors network in such an environment, the impulsive noise must be characterized and studied to predict its evolution. The first observations made during a measurement campaign in power substation indicate impulsive noise RF characteristics depends on the feeding voltage of the equipment. In laboratory, a test bench with impulsive noise sources has been designed and used in order to verify the assumptions made from measurement campaigns and partial discharge theory. Using two impulsive noise specimens, the generator bar and the Tesla-coil, we study the impact of the source voltage and the inter-electrode distance (gap) on the RF characteristics of the emitted impulsive noise. The experiences confirm that, when the feeding voltage increases, the noise becomes more powerful both in time and frequency domains. The same is observed when the gap becomes shorter. Furthermore, the ISM frequency content of impulsive noise also increases, which could severely affect wireless communications.

To satisfy the smart grid electrical network, communication systems in high-voltage substations have to be installed in order to control equipments. Considering that those substations were not necessarily designed for adding communication networks, one of the most appropriate solutions is to use wireless sensor network (WSN). However, the high voltage transported through the station generates a strong and specific radio noise. In order to prepare for such a network, the electromagnetic environment has to be characterized and tests in laboratories have to be performed to estimate the communication performances. This paper presents a method for measuring the noise due to high voltage and more particularly the impulsive noise. In the laboratory, we generate the impulsive noise using two specimens, and we show that these laboratory measurements validate the field measurements of Pakala et al. For the two specimens, it aims to link the noise characteristics (magnitude and frequency) with the specimen parameters (power supply and geometric dimensions) to predict the environments where wireless communications can be troublesome. By using different sets of this measured noise, we show that the statistical model of Middleton Class A can be used to model the impulsive noise in high-voltage substations better than the Gaussian model. We consider a cooperative multiple-input-multiple-output (MIMO) system to achieve the wireless sensor communication. This system uses recent MIMO techniques based on precoding like max-d min and P-OSM precoders. The MIMO precoder-based cooperative system is a potential candidate for energy saving in WSN since energy efficiency optimization is a very important critical issue. Since MIMO precoders are with Gaussian noise assumption, we evaluate the performance of several MIMO precoders in the presence of impulsive noise using estimated parameters from the measured noise.