Abstract-This paper presents a generalized energy storage system model for voltage and angle stability analysis. The proposed solution allows modeling most common energy storage technologies through a given set of linear differential algebraic equations (DAEs). In particular, the paper considers, but is not limited to, compressed air, superconducting magnetic, electrochemical capacitor and battery energy storage devices. While able to cope with a variety of different technologies, the proposed generalized model proves to be accurate for angle and voltage stability analysis, as it includes a balanced, fundamentalfrequency model of the voltage source converter (VSC) and the dynamics of the dc link. Regulators with inclusion of hard limits are also taken into account. The transient behavior of the generalized model is compared with detailed fundamentalfrequency balanced models as well as commonly-used simplified models of energy storage devices. A comprehensive case study based on the WSCC 9-bus test system is presented and discussed.Index Terms-Energy storage system (ESS), transient stability, power system dynamic modeling, electrochemical capacitor energy storage (ECES), superconducting magnetic energy storage (SMES), compressed air energy storage (CAES), battery energy storage (BES).
We study the work cost of processes in quantum fields without the need of projective measurements, which are always ill-defined in quantum field theory. Inspired by interferometry schemes, we propose a work distribution that generalizes the two-point measurement scheme employed in quantum thermodynamics to the case of quantum fields and avoids the use of projective measurements. The distribution is calculated for local unitary processes performed on KMS (thermal) states of scalar fields. Crooks theorem and the Jarzynski equality are shown to be satisfied for a family of spatio-temporally localized unitaries, and some features of the resulting distributions are studied as functions of temperature and the degree of localization of the unitary operation. We show how the work fluctuations become much larger than the average as the process becomes more localized in both time and space.Introduction.-At microscopic scales average quantities no longer characterize completely the state of a system or the features of a thermodynamic process. There, stochastic or quantum fluctuations become relevant, being of the same order of magnitude as the expectation values [1][2][3]. It is therefore important to develop tools that allow us to study the properties of these fluctuations to fully understand thermodynamics at the small scales.One of the best studied quantities in this context is work of out-of-equilibrium processes, and its associated fluctuations. The notion of work is an empirical cornerstone of macroscopic equilibrium thermodynamics. However, work in microscopic quantum scenarios is a notoriously subtle concept (e.g., it cannot be associated to an observable [4]), and although there is no single definition of work distributions and work fluctuations in quantum theory, several possibilities have been proposed (see e.g., [5]). Perhaps the most established notion of work fluctuations is that defined through the Two-Point Measurement (TPM) scheme [6,7], where the work distribution of a process is obtained by performing two projective measurements of the system's energy, at the beginning and at the end of the process. The TPM formalism defines a work distribution with a number of desirable properties: it is linear on the input states, it agrees with the unambiguous classical definition for states diagonal in the energy eigenbasis, and it yields a number of fluctuation theorems in different contexts [1,7,8].An important caveat of this definition is that it cannot be straightforwardly generalized to processes involving quantum fields: projective measurements in quantum field theory (QFT) are incompatible with its relativistic nature. They cannot be localized [9], they can introduce ill-defined operations due to UV divergences and, among other serious problems, they enable superluminal signaling even in the most innocent scenarios [10]. For these reasons, it has been strongly argued that projective measurements should be banished from the formalism of any relativistic field theory [10][11][12]. However, quantum fields are cert...
The paper proposes an approximated yet reliable formula to estimate the frequency at the buses of a transmission system. Such a formula is based on the solution of a steadystate boundary value problem where boundary conditions are given by synchronous machine rotor speeds and is intended for applications in transient stability analysis. The hypotheses and assumptions to define bus frequencies are duly discussed. The rationale behind the proposed frequency divider is first illustrated through a simple 3-bus system. Then the general formulation is duly presented and tested on two real-world networks, namely a 1,479-bus model of the all-island Irish system and a 21,177-bus model of the European transmission system.Index Terms-Frequency estimation, quasi-static phasor model, dq-frame model, transient stability analysis, center of inertia.
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