Related papers: Power System Differential-Algebraic Equations
The increasing complexity of the power grid, due to higher penetration of distributed resources and the growing availability of interconnected, distributed metering devices re- quires novel tools for providing a unified and consistent view…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
This paper proposes to analyze the motion stability of synchro-nous generator power systems using a Lagrangian model derived in the configuration space of generalized position and speed. In the first place, a Lagrangian model of synchronous…
The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive $P({\alpha},{\beta})$ representation of the density operator and the master…
Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
This paper presents a new method for studying electromechanical transients in power systems using three phase, combined transmission and distribution models (hybrid models). The methodology models individual phases of an electric network…
We study the divided power structures over a product of operads with distributive law. We give a systematic method to characterise the divided power algebras over such a product from the structures of divided power algebra coming from each…
Power system state estimation plays a fundamental and critical role in the energy management system (EMS). To achieve a high performance and accurate system states estimation, a graph computing based distributed state estimation approach is…
A new mathematical model for non-equilibrium evaporation/condensation including boiling effect is proposed. A simplified differential-algebraic system of equations is obtained. A code to solve numerically this differential-algebraic system…
Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as…
With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating…
In this paper, the variable wind power is incorporated into the dynamic model for long-term stability analysis. A theory-based method is proposed for power systems with wind power to conduct long-term stability analysis, which is able to…
Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into a number of decoupled oscillators which together behave the same as the original system in an extended neighborhood of the…
The impasse surface is an important concept in the differential-algebraic equation (DAE) model of power systems, which is associated with short-term voltage collapse. This paper establishes a necessary condition for a system trajectory…
In this paper, we propose an energy-based method for the transient stability analysis of a power system transmission switching event. In this method the exit point of pseudo-fault trajectory is used to determine a relevant controlling…
The transition to a new low emission energy future results in a changing mix of generation and load types due to significant growth in renewable energy penetration and reduction in system inertia due to the exit of ageing fossil fuel power…