elk-16-3-6-0808-4[1].pdf

Turk J Elec Engin, VOL.16, NO.3 2008, c

T UBITAK

Power Distortion Issues in Wind Turbine Power

Systems Under Transient States

Tadeusz LOBOS, Jacek REZMER, Tomasz SIKORSKI, Zbigniew WACLAWEK

Wroclaw University of Technology, Department of Electrical Engineering,

Wybrzeze Wyspianskiego 27, 50-370 Wroclaw-POLAND

e-mails: tadeusz.lobos@pwr.wroc.pl

•

jacek.rezmer@pwr.wroc.pl

e-mails: tomasz.sikorski@pwr.wroc.pl

•

zbigniew.waclawek@pwr.wroc.pl

Abstract

In this paper time-frequency methods have been investigated for complex investigations of transient

states in wind power plants. Application of parallel processing in time and frequency domain brought new

ndings in description of wind power plants working under transient conditions. Proposed algorithms

represents standard Short-Time Fourier Transform (STFT) as well as alternative methods associated

with Cohen’s class: Choi-Williams Distribution (CWD) and Zhao-Atlas-Marks Distribution (ZAMD).

In order to explore advantages and disadvantages of the method several experiments were performed

using model of squirrel-cage induction machine connected directly to the grid. Investigated phenomena

concerned power distortion caused by switching-on capacitor banks and faults as well as inuence of wind

speed on instantaneous character of the transient states.

Key Words: Power quality, power system harmonics, time-frequency analysis, wind power plants.

1. Introduction

In the era of technological development power quality issues have more and more crucial meaning. In spite

of achieved experience in specication of distortions, including IEC norms, some cases and accompanying

phenomena require individual approach. In author’s opinion there is still signicant need to extend power

quality specication, e.g. by applying advanced signal processing methods. As examples can use wide

researches on inuence of dispersed energy sources on power quality, especially including wind power plants.

Wind turbines become nowadays regular element of power systems with all its desirable as well as

undesirable inuences. Behind the undisputed signicance of wind power plants for searching the renewable

energy sources there are some aspects which have impact on power quality. One of them is natural result

of variable weather conditions. Another comes from mechanical construction of power plant and power

electronic equipment. Recognizing sources and symptoms of mentioned impacts it can be detailed [1, 2, 3]:

inuence of stochastic wind variation on output torque, power, voltage and current uctuation, periodical

drop of output torque when the mill blade passes the tower (shadow eect), complex, nonlinear oscillation of

the tower and wind turbine which can be transferred to turbine shaft (the frequency of generated oscillation

can attain value from tenth to few Hz), and nally wide spectrum of harmonics in current and voltage caused

by present of power converters.

229

Turk J Elec Engin, VOL.16, NO.3, 2008

Mentioned above mechanical oscillations as well as present of power converters manifest itself in

inuence on grid. The main symptom concerns deterioration of power quality. Recognized phenomena

include voltage sags and ickers, main voltage drops caused by reactive power consumption, power oscillation

in electrical transmission line, wide spectrum of harmonics.

The most signicant meaning have the oscillations of generated power. This problem accompanies

wind power plant both under normal and transient conditions. However, under transient conditions, such

us faults, the range of oscillations is prominent. It must be emphasised that the range of power oscillations

depends on construction of applied generator and load conditions. Wind power plant, working under load

conditions below nominal value, are characterized by considerably higher level of power oscillations than in

case of nominal-load operation. Furthermore, wind power plant tted using asynchronous slip-ring generator

(with controlled resistance in rotor circuit or double-fed) and synchronous generator connected to grid

by power converters, minimize power oscillations in comparison with asynchronous squirrel-cage induction

machines [1, 3].

Selection of proper method for analysis of power distortion in wind turbine system is still actual and

crucial. In [4] we can nd an idea which apply classical Fourier spectrum in order to investigate and classify

power distortion. In this paper the authors propose to apply two-dimensional time-frequency analysis in

order to obtain comprehensive analysis of power distortion. The main known applications of time-frequency

analysis consist speech processing, seismic, economic and biomedical data analysis [5, 6, 7]. Recently some

eorts was also made to introduce time-frequency analysis in electrical engineering area [6 - 10]. The authors

perceive a crucial need for better estimation of distorted electrical signal that can be achieved by applying

the time-frequency analysis [11 - 13].

One of the contributions of this paper is developing a new qualitative method for analysis of transient

phenomena in wind turbine systems. The originality of the paper includes new ndings concerning transient

components of power distortion. Application of proposed methods allowed to compare instantaneous char-

acter of power distortion components, especially appearing under transient conditions with regard for wind

speed. Thanks to proposed approach we can reveal dierence in power distortions in point of its duration

time or contribution of particular frequency components.

In order to explore the eects, grid connected wind turbine system was modelled using Matlab Sim-

PowerSystemToolbox [14]. Selected wind generator structure is squirrel-cage induction machine, connected

directly to the grid. Many of the wind power plants installed today have such conguration. This type of the

generator can not perform voltage control and it absorbs reactive power from the grid. Phase compensating

capacitors are usually directly connected. That type of wind turbine is cheap and robust and therefore

popular, but from the system analysis point of view it has some drawbacks [2, 3, 15].

2. Two-Dimensional Algorithms

The standard method for study time-varying signals is the short-time Fourier transform (STFT), based on

the assumption that, for a short period of time, basis signal can be considered stationary. The spectrogram

utilizes a short-time window h ( τ ) , whose length is chosen so that over the length of the window, the signal

is stationary. The Fourier transform of this windowed signal is calculated to obtain the energy distribution

along the frequency direction at the time corresponding to the centre of the window [7]:

230

LOBOS, REZMER, SIKORSKI, WACLAWEK: Power Distortion Issues in Wind Turbine ...,

+ ∞

STFT x ( t, ω )=

x ( τ ) h ( τ

−

t ) e −jωτ d τ,

(1)

−∞

where t denotes time, ω is angular frequency, τ denotes time lag.

The crucial drawback of this method is that the length of the window is related to the frequency

resolution. Increasing the window length leads to improving frequency resolution but it means that the

nonstationaries occurring during this interval will be smeared in time and frequency [7, 16]. This inher-

ent relationship between time and frequency resolution becomes more important when one is dealing with

signals whose frequency content is changing rapidly. A time-frequency characterization that would over-

come above drawback became a major goal for alternative development based on non-parametric, bilinear

transformations.

The rst suggestions for designing non-parametric, bilinear transformations were introduced by

Wigner, Ville and Moyal at the beginning of nineteen-forties in the context of quantum mechanics area.

Next two decades beard fruit of signicant works by Page, Rihaczek, Levin, Mark, Choi and Williams [17],

Born and Jordan, who provided unique ideas for time-frequency representations, especially reintroduced to

signal analysis [18, 19]. Then in the 1980s, Leon Cohen employed the concept of kernel function and operator

theory to derive a general class of joint time-frequency representation. It can be shown that many bilinear

representations can be written in one general form that is traditionally named Cohen’s class [20].

Cohen dened a general class of bilinear transformation (TFC) introducing kernel function, φ ωt ( θ, τ )[18

- 20]:

+ ∞

x u + τ

x ∗ u

TFC x ( t, ω )=

−

φ ωt ( θ, τ )e jθt e −jωτ e −jθu d u d τ d θ

(2)

−∞

where: t denotes time, ω is angular frequency, τ is time lag, θ is angular frequency lag, and u is an

additional integral time variable.

Performing the transformations brings two dimensional planes which represent the changes of fre-

quency component, here called auto-terms (a-t). Unfortunately, bilinear nature of discussed transformations

manifests itself in existing of undesirable components, called cross-terms (c-t). Cross-terms are located

between the auto-terms and have an oscillating nature. It reduces auto-components resolution, obscures

the true signal features and make interpretation of the distribution dicult. One crucial matter of kernel

function is smoothing eect of the cross-terms with preservation useful properties of designed distribution.

Applying Gaussian kernel in general Cohen’s equation (2) leads to Choi-Williams Distribution (CWD) which

brings mentioned smoothing eect [17, 19]:

+ ∞

4 π

· x u + τ

x ∗ u −

e −jωτ d u d τ

CWD x ( t, ω )=

−

4 ( t−u

τ ) 2

(3)

−∞

Another example is the cone shaped kernel. This approach is associated with Zhao-Atlas-Marks Distribution

(ZAMD) and also brings desirable smoothing eect of the cross-terms. Chosen function h ( τ )servesasthe

231

Turk J Elec Engin, VOL.16, NO.3, 2008

base of two-dimensional cone shaped kernel [18, 19]:

+ ∞

t + |τ|

x u + τ

x ∗ u

e −jωτ d u d τ

ZAMD x ( t, ω )=

h( τ )

−

(4)

−∞

t− |τ 2

3. System Model

A wind turbine generates power and accordingly a mechanical torque on the rotating shaft, while the electrical

machine produces an opposing electromagnetic torque [2]. In steady state operation, the mechanical torque

is converted to real electrical power and delivered to the grid. The power P and torque T generated by the

wind turbine are [2, 3, 15]:

P =

2 ρAC p V 3

(5)

T =

ω s ,

(6)

where: ρ is density of air, A is swept area of the blade, C p is performance coecient, V is wind speed, T

is mechanical torque, P is output power of the turbine, and ω s is rotor speed of the turbine.

At the constant wind speed, coecient C p depends on the rotor speed ω s and pitch angle. The pitch

control dynamic can be neglected in power system transient analysis [15].

The turbine characteristic used in simulation is shown in Figure 1. Figure 2 presents the diagram of the

simulated wind generator system. Simulation was done in Matlab using the SimPowerSystem Toolbox [14].

Simulated generator is a squirrel-cage induction machine rated at 150 kW, 400 V, 1487 rpm. It is connected

to the grid through a Dyg 25/0.4 kV distribution transformer which nominal power equals 1 MVA. Point

of common coupling is connected with the system via typical 5 km overhead line, represented by positive,

negative and zero-sequence of impedance. The system was simulated by equivalent source with short circuit

capacity of 100 MVA and X/R ratio of 7. Capacitor banks provides compensation of absorbed reactive power

and are directly connected.

Figure 1. Characteristic of simulated wind turbine.

232

LOBOS, REZMER, SIKORSKI, WACLAWEK: Power Distortion Issues in Wind Turbine ...,

*%%0,

#%!(

.%!/

'(%

$%&

+,(

Figure 2. Diagram of simulated grid-connected wind turbine system.

4. Investigations

The purpose of investigation was to study the distortion of power generated by wind turbine under transient

states introduced by switching-on capacitor banks and faults. In case of switching-on capacitor banks, the

concern is with phenomena that includes transition from uncompensated to full-compensated state, for xed,

nominal wind speed of 11 m/s. Fault conditions are modelled as 1-phase fault with common coupling ground

point. Simulations of the fault were carried out twice, corresponding to two dierent wind speeds: low-speed

at 8 m/s, and nominal speed at 11 m/s. The wind turbine, presented in Figure 1, is designed to have non-

nominal power ratings P S = -52 kW, and nominal P S = -155 kW, value of generated power. Additionally,

we have assumed that fault appears in steady state with full compensation. Table 1 provides details about

power conditions of investigated wind turbine in steady state as well as values of capacitors, according to

selected wind speed.

Tab l e 1 . Power conditions of the wind turbine in steady state according to wind speed.

Generated

Wind

active

Capacitor

power

8m/s -52 kW 67.2 kVar

11 m/s -155 kW 80.4 kVar

4.1. Switching-on the capacitor banks

One of the investigated phenomena concerns switching-on the capacitor banks, for compensation of reactive

power. Figure 3 shows currents as well as active and reactive power under transition from uncompensated

to compensated state. Analysis of power distortion P were performed using Short Time Fourier Transform,

Choi-Williams Distribution and Zhao-Atlas-Marks Distribution. Observing Figures 4 and 5, we can see two

transient components at 535 Hz and 430 Hz, which aect generated power for about 0.04 s. Additionally,

some advantages of Cohen’s class of distributions can be underline in point of sharp localization of transient

components. In Figure 4 we can observe smearing eect, characteristic for sliding window in STFT method.

Figure 5 conrms sharp detection of transient states when CWD or ZAMD was applied but also indicate

problem of separation for components localized in near time-frequency regions or modulated by peak value.

233

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: