Elsevier

Computers & Electrical Engineering

Volume 78, September 2019, Pages 271-287
Computers & Electrical Engineering

Small-signal stability analysis for two-mass and three-mass shaft model of wind turbine integrated to thermal power system

https://doi.org/10.1016/j.compeleceng.2019.07.016Get rights and content

Abstract

The integration of large wind power into grid affects the power systems dynamics, operation and control. This paper presents the stability analysis of small-signal models of two-mass and three-mass wind turbine interconnected to thermal power system. The use of two-mass/three-mass model is motivated by the need to deal with flexible modes induced due to intermittent varying of wind speed and low speed shaft stiffness. Initially, eigenvalue analysis is performed to investigate the stability of drive train models and also its union model with thermal system. Next, drive train models of wind turbine and its union model are excited by different wind speed profiles. The decomposition of signal into low frequency oscillation (LFO) modes as collection of intrinsic mode functions (IMFs) computed from Hilbert-Huang Transform (HHT) is achieved. The study suggests excitation of LFO modes in drive train models and the same modes in approximate form can be also found in union model with thermal system.

Introduction

The penetration level of wind turbine is increasing throughout world-wide with total installed capacity of 600 GW globally at the end of 2018, according to preliminary data provided by wind word energy association. It is expected that more than 25% of the world electricity will be generated from wind power by 2030 and save more than 3 billion CO2 emission annually [1]. This leads to a major contribution in electrical power grid. However, mechanical resonance of wind turbine occurs frequently, as a matter of fact, the torsional vibration of shaft and the communication between mechanical and electrical systems of wind turbine has received wide concern.

Due to large difference in capacity of WTGS (wind turbine generator system) against thermal power plants, the penetration of high wind power may affect the capacity of load flow distribution, resulting into negative damping effect, which leads to the instability of power grid. The wind turbine models have evolved in wide forms by the researchers in order to investigate its integration to the grid [2], [3]. As penetration level of wind power generation is expected to increase in future, the small-signal stability analysis has been of utmost importance. For analysis of dynamic behavior of WTGS, different types of mass-models like one-mass, two-mass, three-mass and six-mass model have been presented in the past. One-mass model of wind turbine system is not capable to analyze the dynamic behavior of system accurately because it cannot represent the wind dynamics accurately. The modeling of transient behavior of WTGS has been performed using two-mass shaft models [4], [5], [6] and three-mass shaft models [7], [8]. The authors of [9] have presented nonlinear control of variable speed wind turbine using two mass models. Higher mass modeling of drive train creates a computational problem because of number of stages involved. So, for the sake of simplicity, generally two-mass and three-mass drive train are taken into consideration by researchers for analyzing the transient behavior of WTGS.

The authors of [10] have presented an effect of grid side converter current on dynamics of small signal stability using eigenvalue analysis. Additionally, in study, flexible alternating current transmission system devices (FACTS) have been used to examine its impact on system stability. Further, small signal stability of fractional transmission system having offshore wind is presented in [11]. The authors [12] have presented the small signal dynamics of DFIG based wind turbine system in weak ac grid. Further authors [13] have presented an equivalent modeling of wind farm for small signal stability in weak ac network.

Due to highly dynamic characteristics of wind profile, serious issue related to torsional shaft vibration gets induced, resulting into presence of flexible modes. The modal analysis of a grid connected doubly fed induction generator (DFIG) is presented in [14]. The modal analysis concerned to control mode of DFIG is discussed in [15]. Recently authors [16] have proposed the impact of increased penetration of converter control-based generators on power system modes of oscillation.

In the past, small-signal stability analysis of wind power system was presented in [17], [18]. However, impact of using two-mass/three-mass wind turbine model integrated to thermal power system and their induced mode analysis due to wind dynamics as small-signal stability analysis has not been discussed much. The authors of [19] have presented the modal analysis of grid connected DFIG, with focus on the detailed mechanical structural modeling of the wind turbine. The power system dynamics of the generator with the mechanical-electric coupling of the system has been presented in [20]. It is obvious that a large number of wind generators are going to be connected with existing power grid in near future to fulfill the load requirement. Therefore, it is important to analyze the stability of power system, including wind turbine generator system. Further, Authors of [21] have presented a novel coordinated control approach for high penetration of wind energy in smart grid.

In this work, an effort has been made to show the stability issues in small-signal modelling of two-mass and three-mass wind turbine system integrated to thermal-thermal system. The model based on small signal stability analysis is used to study the wind turbine shaft torsional vibration. Due to this reason, this work concentrates on union model of wind turbine system and thermal power system.

In this paper, we propose a new approach to analyze the induced flexible modes in two-mass/three mass wind turbine drive model integrated to thermal power system and its union model-based drive train system. In order to find low frequency oscillation (LFO) signal, Hilbert-Haung Transform (HHT) is applied to analyze the oscillatory modes present in the signals (shaft torque and frequency deviation in area-1 and area-2). Further, two different wind profile have been considered in this study to evaluate the vibrational mode excitation for two-mass /three-mass and its union model. The stability analysis of two-mass, three-mass and its union models is performed using eigenvalue analysis. In order to analyze the relation among the system state variables, participation factor is calculated which gives the relation between modes and corresponding variables. Further, location of poles is also determined for investigation of stability of the system.

The paper is organized as follows. Section II describes the small-signal modelling and stability of thermal power system connected to wind turbine. Section III, describes the modelling of wind profile followed by modal analysis using EMD in section IV. Section V presents the small signal analysis of system. Section VI discusses simulation results on study system. Finally, conclusion is given in section VII.

Section snippets

Small–signal modelling and stability of thermal power system connected to wind turbine

The schematic diagram of wind turbine integrated to thermal power system (two-area) is shown in Fig. 1. The output power of WTGS is fed to thermal power system in area-1. The frequency deviation will occur in each area due to mismatch between total generation and load demand. To study the torsional effects in wind turbine model, a small signal stability model is needed.

Modeling of wind profile

The intermittent property of wind profile is modeled in this section. Vander-Hoven [23] is used in this study to model the wide band variation in wind speed. The spectral power of wind speed is computed in range from 0.0007 to 900 cycle/hours. The numerical wind speed procedure based on sampling the spectrum of wind is developed in [23]. Consider ω0, i = 1 to (N + 1) is discrete angular frequency and Pvvi) the corresponding power spectral density.

The harmonic frequency amplitude is

Mode analysis technique using EMD

This section describes the steps adopted to analyze the LFO signals using EMD technique.

Step 1: In the first step, the signal is decomposed into sets of intrinsic mode function [IMFs] using EMD method.

Step 2: Compute the instantaneous frequency and amplitude of each IMF using HHT algorithm. After computation of IMFs via EMD, apply Hilbert transform [HT] to the interested IMF. The oscillation mode for the physical characteristics of signal can be represented in complex form as:z(t)=x(t)+iy(t)=A(t

Hilbert Transform (HT)

Hilbert transform is actually the relationship between the real and imaginary parts of fast fourier transform [FFT] of one-sided function. Hilbert transform H[s(t)] of a signal s(t) is given by:H[s(t)]=s(τ)s(tτ)dτwhere, t is time and τ is translation parameter.

Hilbert transform is a frequency independent time domain involution that maps real time-domain value into another value. It is also called 90° phase shifter and does not affect non-stationary characteristic of a modulating signal.

Small-signal analysis

To study the dynamic behavior of drive train model and its union model integrated to thermal power system, eigenvalue analysis and participation factor is computed to know the relation between modes and state variable. In this section, eigenvalue analysis of two-mass/three-mass and its union model is presented.

Simulation results and discussion

In this section, dynamic simulation results of drive train WT model connected to thermal-thermal system with wind variation is discussed. The flexible modes induced in generator shaft and frequency deviation of each area are analyzed. The details are given in following subsections.

Conclusions

In this study small-signal stability analysis for WT system based on different drive train models (two-mass/ three-mass model) and its union model with integration of thermal power system is investigated. The detail state space modelling is performed for various case studies. The stability study at initial stage was performed using eigenvalue analysis. Further to know the exact relation between modes and corresponding state variable, participation factor was computed. The understanding on

Conflict of interest

None.

Vijay Pratap Singh received the Ph.D. degree from Motilal Nehru National Institute of Technology, Allahabad Prayagraj, India. Currently he is an Assistant Professor in the Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P. India. His research area includes robust control applications in load frequency control and power quality in distributed generations, Smart grid technologies and renewable energy resources.

References (25)

  • B. Boukhezzar et al.

    "Nonlinear control of a variable-speed wind turbine using a two-mass model”

    IEEE Trans Energy Convers

    (2011)
  • R. Bhushan et al.

    Effects of parameter variation in DFIG-based grid connected system with a FACTS device for small-signal stability analysis

  • Cited by (0)

    Vijay Pratap Singh received the Ph.D. degree from Motilal Nehru National Institute of Technology, Allahabad Prayagraj, India. Currently he is an Assistant Professor in the Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P. India. His research area includes robust control applications in load frequency control and power quality in distributed generations, Smart grid technologies and renewable energy resources.

    Nand Kishor received the Ph.D. degree from Indian Institute of Technology (IIT), Roorkee, India. Currently he is Professor in the Department of Electrical Engineering, Motilal Nehru National Institute of Technology (MNNIT), Allahabad, India. His research area includes AI applications in power system, Wireless sensor systems, Distributed generation with renewable resources, WAMS, Smart grid technologies.

    Paulson Samuel received the Ph.D. degree from NIT, Allahabad, India. Currently he is Professor in the Department of Electrical Engineering, Motilal Nehru National Institute of Technology (MNNIT), Allahabad, India.His research area includes Renewable Energy and Grid Interface, Power Converters, Power applications in Power Systems, Power Quality.

    Navdeep Singh received the Ph.D. degree from Motilal Nehru National Institute of Technology, Allahabad Prayagraj, India. Currently he is working as an Assistant Professor in the Department of Electrical Engineering, Madan Mohan Malvyia University of Technolgy Gorkahpur, UP, India. His research area includes renewable energy, power electronics and Power converters.

    This paper is for regular issues of CAEE. Reviews processed and recommended for publication to the Editor-in-Chief by Associate Editor Dr. A. H. Mazinan.

    View full text