Quadratized Three-Phase Induction Motor Model for Steady-State and Dynamic Analysis

Abstract

equations of a power system. Thus the model can be Abstract-This paper describes the implementation of a three-immediately used for steady-state (load flow) analysis for both phase, phase-domain induction motor model for asymmetric load transmission and distribution systems. The model optionally flow and quasi-steady state analysis. The mathematical model is includes rotor parameters that are speed-dependent and vary based on the use of linear and quadratic equations, reducing es oto eterat are sped-dpenen andfvar therefore the system nonlinearity to at most second degree. The depending on the operating point. Ths allows a unified model optionally includes slip-dependent rotor parameters, representation of allmotortypes anddesigns including double allowing therefore a unified and accurate representation of every cage models or deep bar rotor models. Augmentation of the possible motor design (NEMA designs A, B, C and D). A model with appropriate dynamic equations allows its use in parameter estimation methodology is also presented that allows quasi-steady state analysis, as well, with practically very little the motor model identification using the slip-torque and slip-model modification, which enables capturing dynamic events current motor characteristic. The estimation procedure and the model performance for both steady-state and dynamic analysis inesystem. are demonstrated with some simple numerical examples. One of the main problems with induction motor Index Terms-Induction motor model, Load flow analysis, representation is the unavailability of parameter values toParameter estimation, Quasi-steady-state analysis, Three-phase construct accurate models. This is one of the reasons motors modeling are not usually explicitly represented in system studies. The issue of induction motor parameter estimation has been addressed by several researchers [9]- [24]. In many of these I. INTRODUCTION cases high accuracy is demanded in the parameter T HIS paper addresses the issue of induction motor determination, when the problem is viewed from the electric modeling and model estimation for power system analysis machinery point of view [9]-[16]. However, when load studies. Load modeling in power systems is of great modeling is concerned for power system analysis applications importance, for both steady-state and dynamic analysis, and (like load flow analysis, stability analysis, dynamic simulation has been addressed extensively in literature [1][2][3][4][5][6][7][8]. Induction or power system protection coordination) the level of accuracy motors constitute the most significant part of industrial load needed is considerably less, of the order of 10-15% [17]. Field and their performance has a considerable impact on the measurements after specific tests can be used for accurate behavior of a power system. Nevertheless, power system motor model estimation, however such test are usually analysis studies usually refrain from explicitly representing difficult or impossible to perform in actual, operational induction motor loads, an...

Hierarchical optimization and control of a power system

“…First, the mathematical model of the device is formulated as a set of differential and algebraic equations in terms of the state and control variables. Next, the model is quadratized [7]- [9]; any nonlinear equation above degree two is reduced to degree not higher than two by introducing new variables. Afterward, the resulting differential and algebraic equations are integrated using the quadratic integration method based on [10], which is based on three point collocation method, to convert these equations into a set of algebraic quadratic equations.…”

Hierarchical optimization and control of a distribution system

“…To make the process autonomous, an object oriented approach is used for the estimation process. In this method, each device in the system is expressed in a generic device format (1) after the quadratization process [11]- [13] is performed on the mathematical model of the device.…”