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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
Fano interference or coherent population trapping applied to optically dense media. electromagnetics the study of the effect of electric charges at rest and in motion. electromechanical equation a basic non-linear equation that governs the rotational dynamics of a synchronous machine in stability studies. The equation is given by 2H d 2 /s dt 2 where H is a constant defined as the ratio of the kinetic energy in megajoules at synchronous speed to the machine rating in MVA, s is the synchronous speed in rads per second, and is the load angle expressed in electrical degrees. Various forms of the swing equation serve to determine stability of a machine within a power system. Solution of the swing equation yields the load angle as a function of time. Examination of all the swing curves (plot of w.r. to time) shows whether the machines will remain in synchronism after a disturbance. See also swing equation. electromechanical relay a protective relay that uses electrical, magnetic, and mechanical circuits to implement the operating logic.
Power System Stability
Published in Syed A. Nasar, F.C. Trutt, Electric Power Systems, 2018
These various forms of the swing equation are used according to the nature of the problem at hand. Having formulated the governing equation for δ, to investigate the stability of the machine, we solve for δ as a function of time. A plot of δ(t) is known as the swing curve, a study of which often shows if the machine will remain in synchronism after a disturbance. The swing equation contains information regarding the machine dynamics and stability. However, it is important to realize that we made two basic assumptions in deriving it: (1) In (6.2) we took M to be constant, although, strictly speaking, this is not so; (2) the damping term proportional to dδ/dt has been neglected.
Philosophy of Security Assessment
Published in James A. Momoh, Mohamed E. El-Hawary, Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, 2018
James A. Momoh, Mohamed E. El-Hawary
This chapter dealt with the philosophy of security assessment based on frequency domain models and equal area criterion concepts. In particular, we define the conventional ingredients for power system stability including applications of the swing equation and its alternate forms.
Maximum Basin Stability Principle for Synchronization Stability Control of Smart Grid
Published in Electric Power Components and Systems, 2018
The power grid consisting of generators and loads connected by the transmission lines is modeled by using the classical swing equation system (see refs [5] and [6] for a detailed derivation) where . , and are the phase, angular frequency, and magnitude of the voltage vector for generator i, measured under reference that co-rotates with the grid’s rated frequency . Furthermore, is the cumulative moment of inertia of the masses denoted by node i, is their cumulative power injection, is the amount of power used or injected by constant consumers and renewable generation devices and is the net injected power. Based on the balance of active power, the model incorporates frequency dynamics but neglects voltage dynamics under the assumption of perfect reactive power control. It is noted that Eqs. (1) and (2) formally correspond to the second-order Kuramoto model [25].
Assessment of the optimum location and hosting capacity of distributed solar PV in the southern interconnected grid (SIG) of Cameroon
Published in International Journal of Sustainable Energy, 2023
Chu Donatus Iweh, Samuel Gyamfi, Emmanuel Tanyi, Eric Effah-Donyina
Ignoring the damping coefficient (i.e. D = 0) and substituting Equation (18) in (16), it gives; Equation (19) presents the dynamics of the rotor in a synchronous generator and it is called the swing equation.
Optimisation and adaptation of synchronisation controllers for networked second-order infinite-dimensional systems
Published in International Journal of Control, 2019
Michael A. Demetriou, Fariba Fahroo
The problems of synchronisation and consensus through feedback for distributed parameter systems have been considered starting with the work by Demetriou (2009, 2010, 2012, 2013a, 2013b). Relevant works such as Ambrosio and Aziz-Alaoui (2012) and Li and Rao (2013) considered controllability aspects and convergence properties for distributed parameter systems. Ambrosio and Aziz-Alaoui (2012) considered coupled reaction-diffusion systems of the FitzHugh--Nagumo type and classified their stability and synchronisation. Li and Rao (2013) considered coupled hyperbolic partial differential equations (PDEs) and proposed a synchronisation scheme through boundary control. Specifically, the work in Ambrosio and Aziz-Alaoui (2013), Li, Chen, Xu, and Wang (2015), and Wu and Chen (2012) examined the synchronisation of coupled advection-diffusion PDEs with full state-feedback synchronisation controllers. A similar framework for coupled PDEs was considered in Wang, Teng, and Jiang (2012), where an array of linearly coupled neural networks with reaction-diffusion terms and delays was examined. Related work that considered coupled PDEs with an a-priori-defined coupling in the form of diffusive coupling examined various aspects of stability and control (Wu & Chen, 2012). Similar in flavour are the works in Arcak (2012), Shafi and Arcak (2014), and Shafi, Arcak, Jovanović, and Packard (2013) in which networked systems interact through a diffusive coupling and the problems of synchronisation and pattern formation and the subsequent adaptation of the local interconnection strengths are considered. A final aspect comes from modelling the average consensus algorithm as an advection-diffusion process governing the homogenisation of fluid mixtures (see Sardellitti, Giona, & Barbarossa, 2010). This interaction that is related to the diffusive coupling was considered in Arcak (2012), Shafi and Arcak (2014), and Shafi et al. (2013). Synchronisation of systems, finite or infinite, that consider second order in time dynamics, finds applications in power networks. Recent work in Li, Djouadi, and Tomsovic (2012) considered the PDE framework for stability of smart grids with communications based on the swing equation (Thorp, Seyler, & Phadke, 1998). A survey of the multitude of applications in various scientific disciplines, including biology and social networks for coupled second-order (finite-dimensional) systems, was presented in Dörfler and Bullo (2014). Earlier works by the same authors considered the swing equation as the limiting case of the Kuramoto oscillators (Dörfler & Bullo, 2011, 2012), and studied the critical coupling and transient stability in power networks.