This chapter is about measuring voltage and current waveforms as well as power quality. Waveform sensors can show the wave shape of voltage and current; as opposed to only their RMS values, or only the phasor representation of their fundamental components. We discuss event-triggered waveform capture, and also measuring distortions in voltage and current waves, including harmonics, inter-harmonics, and notching. We cover event detection, event capture, and statistical analysis of events in waveform measurements, event signature evaluation, event classification, and pattern recognition. Another important subject in this chapter is the analysis of faults and incipient faults. This includes the analysis of fault signatures, faults in underground power cables, overhead power lines, transformers, capacitor banks, and distributed energy resources. We also discuss harmonic synchrophasors and their applications in harmonic state estimation and topology identification. Synchronized waveform measurements, waveform measurement units, synchro-waveforms, and their applications are also covered. Finally, we discuss accuracy in waveform measurements, and the impact of noise and interference.

This chapter is about measuring voltage and current. The use of instrument transformers and also an emerging alternative option to measure current and voltage without electric contact are discussed. Basic concepts, such as sampling rate, reporting rate, measurements accuracy, measurement aliasing, and the impact of averaging filters are covered. Root-Mean-Square (RMS) voltage and current profiles are examined; as time series and in histograms and scatter plots. RMS voltage and current transient responses, which can be caused by faults, equipment actuation, and load operation are discussed. RMS voltage and current oscillations are studied, such as in wide-area oscillations. Three-phase RMS voltage and current measurements; and some applications, such as measuring phase unbalance and phase identification are discussed. The fundamental subject of events in smart grid measurements is partly covered in this chapter. Events can be caused by a change in any component in the power system. Methods for event detection are discussed. Other subjects that are covered in this chapter include measuring frequency, the frequency responses of the electric grid; and measuring frequency oscillations.

This chapter is about the use of probing techniques in smart grid sensing. Probing is the broad technique of perturbing the power system to achieve enhanced monitoring capabilities. Rather than only passively collecting measurements, probing methods make use of various grid components to actively create opportunities to learn more about the power system and its unknowns. We explore the applications of probing in state and parameter estimation to enhance observability and redundancy. Applications of probing in topology identification, phase identification, model-free control, and repeatable modal analysis are also discussed. Examples of creating the probing signal, such as by using resistive brakes or intermittent wave modulation are explained. We also discuss the use of power line communications as a probing tool to diagnose incipient faults and locate faults in power cables. Applications of probing via power line communications are discussed also in topology identification and phase identification.

The purpose of this chapter is to provide the background knowledge that will be useful throughout this book. First, we do an overview of the field of smart grids. We discuss why we need to study smart grid sensors. Next, we provide an overview of the basics of electric power systems and the power grid. The subjects that are covered in this chapter are sufficient that this book can be used by a reader whose background is not in power engineering.

This chapter is about measuring voltage and current phasors and synchrophasors. Phasor calculation, time synchronization, data concentration, and different types of phasor measurement units are discussed. Measuring phase angles, impact of the changes in the system frequency on measuring phase angles, and the applications of phase angle measurements are covered. Measuring the rate of change of frequency and the applications of synchronized frequency measurements are discussed. Relative phase angle difference and phasor differential and their applications, such as in the analysis of wide-area oscillations; and in identifying the location of events are explored. Analysis of events in phasor measurements; including feature selection and classification are covered. Three-phase phasor measurements, unbalanced phasor events, phase identification, and the application of symmetrical components are discussed. State estimation, parameter estimation, and topology identification in power systems using phasor measurements are presented. Other subjects that are covered in this chapter include accuracy in phasor measurements, performance classes, steady-state performance, and dynamic performance.

In this chapter, the characteristics of pulse propagation in an isotropic and spatially homogeneous Kerr medium are discussed. The general optical pulse propagation equation and its form under the rate equation approximation are presented in the first section. The second section addresses the effect of dispersion on the propagation of an optical pulse in a linear optical medium where the nonlinear susceptibility does not exist. The third section addresses the effect of self-phase modulation on the propagation of an optical pulse in a nonlinear optical Kerr medium without the effect of dispersion. The following two sections cover the phenomena and characteristics of spectral stretching, pulse stretching, pulse compression, soliton formation, and soliton evolution that appear under different conditions in the propagation of an optical pulse in a nonlinear optical Kerr medium with the effect of dispersion. The final section addresses the process of modulation instability from the viewpoint of nonlinear wave propagation.

The optical response of a material is described by an electric polarization through an optical susceptibility. In the presence of optical nonlinearity, the total optical susceptibility is generally a function of the optical field. When the electric polarization can be expressed as a perturbation series of linear and nonlinear polarizations, field-independent linear and nonlinear susceptibilities can be defined. The linear susceptibility is a second-order tensor, and the second-order and third-order nonlinear susceptibilities are respectively third-order and four-order tensors. Each tensor element of these susceptibilities satisfies the reality condition. All tensor elements as functions of interacting optical frequencies generally possess intrinsic permutation symmetry. A full permutation symmetry exists when the material causes no loss or gain at all of the optical frequencies, and Kleinman’s symmetry exists when the medium is nondispersive at these frequencies. The spatial symmetry of a linear or nonlinear susceptibility tensor depends on the structure of the material.

This chapter gives a short summary of mathematical instruments required to model sensor systems in the presence of both deterministic and random processes. The concepts are organized in a compact overview for a more rapid consultation, emphasizing the convergences between different contexts.

Optical interactions can generally be categorized into parametric processes and nonparametric processes. A parametric process does not cause any change in the quantum-mechanical state of the material, whereas a nonparametric process causes some changes in the quantum-mechanical state of the material. Phase matching among interacting optical fields is not automatically satisfied in a parametric process but is always automatically satisfied in a nonparametric process. All second-order nonlinear optical processes are parametric in nature. The nonlinear polarization and phase-matching condition of each second-order process are discussed in the second section. Some third-order nonlinear optical processes are parametric, and others are nonparametric. The nonlinear polarization and phase-matching condition of each third-order process are discussed in the third section.

Stimulated Raman scattering leads to Raman gain for a Stokes signal at a frequency that is down-shifted at a Raman frequency, and stimulated Brillouin scattering leads to Brillouin gain at a frequency that is down-shifted by a Brillouin frequency. This chapter begins with a general discussion of Raman scattering and Brillouin scattering. After a discussion of the characteristics of the Raman gain, Raman amplification and generation based on stimulated Raman scattering are addressed through their applications as Raman amplifiers, Raman generators, and Raman oscillators. After a discussion of the characteristics of the Brillouin gain, Brillouin amplification and generation based on stimulated Brillouin scattering are addressed through their applications as Brillouin amplifiers, Brillouin generators, and Brillouin oscillators. This chapter ends with a comparison of Raman and Brillouin devices.

The general formulation for optical propagation in a nonlinear medium is given in this chapter. In the first section, the general equation for the propagation in a spatially homogeneous medium is obtained. This equation can be expressed either in the frequency domain or in the time domain. In the second section, the general pulse propagation equation for a waveguide mode is obtained in the time domain. In the third section, the propagation of an optical pulse in an optical Kerr medium is considered for three useful equations: nonlinear equation with spatial diffraction for propagation in a spatially homogeneous medium, nonlinear Schrödinger equation without spatial diffraction for propagation in a spatially homogeneous medium or in a waveguide, and generalized nonlinear Schrödinger equation for the nonlinear propagation of an optical pulse that has a pulsewidth down to a few optical cycles or that undergoes extreme spectral broadening.

This chapter presents a general overview of sensor characterization from a system perspective, without any reference to a specific implementation. The systems are defined on the basis of input and output signal description and the overall architecture is discussed, showing how the information is transduced, limited, and corrupted by errors. One of the main points of this chapter is the characterization of the error model, and how this one could be used to evaluate the uncertainty of the measure, along with its relationship with resolution, precision and accuracy of the overall system. Finally, the quantization process, which is at the base of any digital sensor systems, is illustrated, interpreted, and included in the error model.