Simulation of directly grid-connected wind turbines for voltage fluctuation evaluation.
Power and voltage generated by a wind turbine are more variable than that produced by conventional generators. Therefore, with the increasing penetration of wind energy into the grid, it is very important to simulate precisely the wind turbine/grid interaction to evaluate voltage fluctuation and other power quality aspects. In this paper, the wind turbine instantaneously generated power and voltage at the point of common connection (PCC) with grid are simulated by considering all the aerodynamical and mechanical effects, which could affect them. The inherent effect of the wind speed on the entire blade swept area is simulated in the model of the wind speed. This model takes into account the effects of tower shadow and the rotational sampling of turbulence. The generated power is obtained by the simulation of the wind speed time series into a wind turbine model. The proposed wind turbine model includes detailed sub-models of aerodynamic rotor, drive train and ac generator. A dq arbitrary reference frame is used for modeling of asynchronous generator. The flux variations in the stator circuit are involved. The flickermeter model which expresses voltage fluctuations is simulated according to the IEC standard 61000-4-15. The wind speed, wind turbine and flickermeter models are simulated in Matlab/Simulink software. Both of grid and site parameters, which affect voltage fluctuation, are investigated. These parameters have a wide influence on voltage fluctuation and flicker emission levels.
Wind turbine generators are increasingly becoming among the prominent components of power systems. Due to the stochastic nature of wind, electrical power delivered by this type of generation possesses similar features. Furthermore, wind turbines are usually integrated with the grid at remote terminals, far from central loads or conventional generation. This is raising certain reluctance on the part of utility companies to inject that source of power with unknown behavior and to evaluate the accompanied power quality considerations. Due to the importance of wind-turbine power quality considerations, standard IEC 61400-21  provides procedures for determining the power quality characteristics of wind turbines.
The sources of fluctuations in the generated power are due to stochastic aspects that determine wind speed at different times and heights, and to deterministic or periodic effects. The largest periodic effect known as the tower shadow is at the frequency at which rotor blades pass by the tower. In the common three bladed horizontal axis wind turbines, this frequency is known as a 3p frequency which is three times the rotational frequency . The reactive power consumption of the wind turbine asynchronous generator depends on the active generated power. The drawn reactive power increases with the increase of the generated active power. Therefore, the reactive power consumption of the generator fluctuates as the wind speed fluctuates. Due to the fluctuations in the active and reactive power, the voltage at PCC fluctuates.
Voltage fluctuation is a serious issue particularly for direct-connected wind turbines because these turbines produce power dependent on the variations of the wind speed and inject it without conditioning into the grid. Voltage fluctuation disturbs the sensitive electric and electronic equipment. This may lead to a great reduction in the life span of most equipment . The lighting flicker level is generally used to measure voltage fluctuation. A case studying the voltage level profile when the power system is integrated with wind generation is given . The influence of wind turbines on consumer voltage quality is studied . A frequency domain approach to wind turbines for flicker analysis is presented .
The need to accurately simulate the wind turbines and investigate their interaction with the grid is becoming so important, since the penetration of wind in certain areas reaches significant levels. A suggested nonlinear simulation depending on the collected measured data is presented . This simulation employs the neural network technique to predict the wind turbine output power. The modeling of wind turbines for power system studies is presented . The aerodynamic loads of the wind turbines are represented and simulated in frequency domain . A comprehensive model of mechanical part consists of a number of lumped inertias, elastically coupled to each other is presented , . The problem in this model that it needs more manufacturer's design data about turbine elements which is not available in most cases. Soft tools and techniques used for modeling and design simulation of wind turbines are reviewed . A simple approach to aggregated wind farm equivalent for the analysis of power system operation is presented .
This paper presents the comprehensive time-domain modeling of wind speed, wind turbine and flickermeter and investigates the influence different factors on voltage fluctuation caused by wind turbines. The wind speed model considers the effects of tower shadow and the interaction of blade rotation with wind turbulence. The wind turbine model is composed of three sub models connected together, aerodynamic rotor, drive train and induction generator models. A soft shaft along with the mass inertia of both the generator and wind turbine rotors is simulated in a 2-mass drive train model. The induction generator model, in the dq0 arbitrary reference frame, involves the transients in the stator circuit. The flickermeter is implemented according to the IEC standard 61000-4-15 . The wind speed, wind turbine and flickermeter models are implemented in Matlab/Simulink. The wind speed produced from wind speed model is applied to the aerodynamic model to extract the aerodynamic torque. This torque is fed to the drive train/generator models to simulate the electrical power from wind turbine.
The wind speed, wind turbine and flickermeter models are explained in the following sub-sections.
Wind Speed Model
The main idea in the wind speed model is to represent the interaction of turbine blades with wind speed distribution over the rotor swept area by an equivalent time series data at hub level. The equivalent time series data simulates the wind and when it is applied to a specific aerodynamic model, it reproduces the aerodynamic torque from a wind turbine.
Equivalent wind speed ([W.sub.eq]), produced from wind speed model, takes into account the deterministic and stochastic wind speed actions on the rotor area. The [W.sub.eq] is given as follows ;
[W.sub.eq] (t, [psi]) - [U.sub.eq-det] ([psi]) + [U.sub.eq-sto] (t, [psi]) (2)
[U.sub.eq-det] is the deterministic part of the wind speed;
[U.sub.eq-sto] is the stochastic part of the wind speed;
[psi] is swept angle of the rotor blades; and
t is the time.
The deterministic part of the wind is time independent and it depends only on the rotor position, [psi]. It consists of the mean wind speed, tower shadow and wind shear. The wind shear is very important to the analyses of blade loads but it is not transmitted to the electrical power so it is neglected. The deterministic part components are explained in the following items.
a) Mean wind speed
The mean wind speed is estimated from the site wind data or wind Atlas. It is converted from its measuring level to the wind turbine hub level according to the following formula ;
[U.sub.o] = ([h.sub.o]/[h.sub.1])[g.sup.*] x [W.sub.1] (2)
where: [W.sub.1] is the average wind speed measured at height [h.sub.1];
[U.sub.o] is the mean wind speed at hub level, [h.sub.o];
[g.sup.*] is an exponent varying from (0.16 to 0.40).
[g.sup.*] = 0.16 for open land with a few obstacles and [g.sup.*] = 0.4 for land with big obstacles).
b) Tower shadow
Towers, in horizontal axis wind turbines, are obstacles to the free wind that modifies the wind flow. The upstream flow, which is interested in this paper, is reduced in front the tower and increased laterally. The model is limited to the effects on horizontal, up-wind, and three-bladed wind turbines. When the rotor blade crosses the tower, a drop in the aerodynamic torque will be occurred. Consequently, the Fourier transformation of the aerodynamic torque influenced by tower shadow shows the 3np (i.e., 3p, 6p, 9p, ....) components included in it. The wind turbine dynamics remove the higher 3np frequency components from the electrical output power and the dominant frequency of tower shadow is 3p . Hence, the simulation of deterministic part of wind speed model is illustrated as block diagrams in Fig. 1 . Where "[U.sub.det-3]" is the contribution amplitude of the tower shadow, "[U.sub.o]" is the mean wind speed and "[U.sub.eq_det]" is the output deterministic wind speed.
[FIGURE 1 OMITTED]
The stochastic part depends on both the time and the rotor position, [psi]. Low frequency wind variations have large amplitudes and vice versa. To model this characteristic, the Kaimal spectral description of turbulence signal, K(f), is commonly used , . Equation (3) defines the Kaimal turbulence filter model.
f.K(f) /[[sigma].sup.2] = f.[X.sub.L]/[U.sub.o]/[(1+[1.5.sup.*] (f.[X.sub.L]/[U.sub.o])).sup.5/3] (3)
Where: f is the frequency of the turbulence;
[x.sub.L] is the turbulence length scale; and
The interaction between the rotation of wind turbine blades and the variable wind speed due to wind turbulences is called the rotational sampling of turbulence. The rotational sampling of turbulence has been reported as the main cause of flicker from wind turbines. Therefore, the contribution of rotational sampling of turbulence on wind speed model is very necessary.
The stochastic part, which includes the rotational sampling turbulence, is simulated by same way of deterministic component and depends mainly on (0p and 3p harmonic). However, the amplitudes are time dependent as shown in Fig. 2. The turbulence is simulated by random numbers filtered by Kaimal filter to eliminate high frequency components. Two second-order filters are employed as admittance functions for the smoothing of the amplitudes of 0p and 3p harmonics after applying Kaimal filter .
The [W.sub.eq] is the sum of the stochastic and deterministic parts as presented in Eqn. 1.The rotor position, [psi], is obtained from the integral of the angular rotor speed.
[FIGURE 2 OMITTED]
Wind Turbine Model
The wind turbine structure is generally composed of the rotor blades, a mean of drive train, and the electrical generator. In this paper, the rotor blades have been connected to an induction generator through a flexible coupling followed by gear box. The induction generator is directly connected to the grid. The dynamic wind turbine parameters of a fixed-speed, stall-regulated wind turbine are investigated. Figure 3 shows a layout of the proposed wind turbine model. Each sub-model presented in Fig. 3 will be given in the following sub-sections.
[FIGURE 3 OMITTED]
Aerodynamic Rotor Model
The aerodynamic rotor converts the wind into mechanical torque. The aerodynamic model uses the [W.sub.eq] and the rotor speed as input data to compute the aerodynamic torque on the wind turbine shaft. The aerodynamic torque, [T.sub.aer], can be expressed in (4) .
[T.sub.aer] = [rho] x [pi]* [R.sup.2] x [W.sup.3.sub.eg] x [C.sub.p]([lambda])/ 2 [(omega).sub.wtr] (4)
[[rho].sub.x] is the air density;
R is the rotor radius;
[C.sub.p]([lambda]) is the power coefficient of stall regulated wind turbine;
[[omega].sub.wtr] is the rotational rotor speed.
[lambda] is the tip speed ratio (R x [[omega].sub.wtr] / [W.sub.eq]).
Drive Train Model
The drive train model simulates the elastic connection between the low-speed wind turbine shaft and the high-speed generator shaft. It consists of the inertia of both the turbine and generator (2-mass system). The elastic coupling between the two masses is modeled by spring, k, and damper, B. The equivalent model for the drive train of the wind turbine referred to the generator side is shown in Fig. 4.
[FIGURE 4 OMITTED]
The dynamics of the drive train on the generator side can be written in (5) and (6) :
[T.sub.aer] = [J.sub.T] d[[omega].sub.wtr]/dt + k x [DELTA]v + B x [DELTA][omega]) (5)
k x [DELTA]v + B x [DELTA][omega]) = [J.sub.G] d[[omega].sub.g]/dt + [T.sub.e] (6)
Where: [DELTA][omega] = [[omega].sub.wtr] - [[omega].sub.g]
[DELTA]v = [v.sub.wtr] - [v.sub.g]
[[omega].sub.wtr] = d[v.sub.wtr]/dt and [[omega].sub.g] = d[v.sub.g]/dt
[J.sub.T] (kg x [m.sup.2]) is the turbine moment of inertia,
[J.sub.G] (kg x [m.sup.2]) is the generator moment of inertia,
k (N x m/rad) is the stiffness of the shaft,
B (N x m x sec/rad) is the absorption of the shaft,
[T.sub.aer] (N x m) is the wind turbine torque,
[T.sub.e] (N.m) is the electromagnetic generator torque,
[[omega].sub.wtr], [[omega].sub.g] (rad [s.sup.-1]) are the angular speed of the turbine and of the generator, respectively, and [v.sub.wtr] [v.sub.g] (rad) are the positions of the turbine and generator shafts, respectively.
Induction Generator Model
The asynchronous machine has been used as generator for many years in wind turbines. This type of machine has high reliability, low price, and low maintenance. The speed flexibility (slip), when compared to the synchronous machines reduces the current spikes due to wind gusts. The main disadvantage is that asynchronous machine consumes reactive power, which influences the wind turbine/grid integration in normal and transient conditions. A dq arbitrary reference frame is extensively used for modeling of several types of induction generators , , . In this model the dynamic equations of induction machine in the dq0 arbitrary reference frame are employed. The variations in the stator circuit are involved.
Flicker is defined as "impression of unsteadiness of visual sensation induced by a light stimulus whose luminance or spectral distribution fluctuates with time" . The flicker level depends on the amplitude, shape and repetition frequency of voltage fluctuation. Flicker level is measured by the use of a flickermeter described in IEC 61000-4-15 . The flickermeter takes voltage as input and gives the short-term flicker index, [P.sub.st], as output. The flickermeter sequence consists of five steps;
--Step1: input voltage adaptor
--Step2: square law demodulator
--Step3: weighting filters
--Step4: squaring and smoothing
--Step5: statistical manipulation
The steps 1-4 are simulated in Matlab/simulink. The output of step 4 is the instantaneous flicker level (IFL). Using the statistical manipulation over IFL for an observation period of 10 min, the [P.sub.st], can be estimated. The normalized response of the flickermeter (Fig. 5) shows that a quite small voltage fluctuation at certain frequency (8.8 Hz) can be irritable.
The integration of wind turbines with the distribution networks may affect different issues of power quality. The flicker level ([P.sub.st][less than or equal to]1) can be a limiting condition for connecting wind turbines to low voltage networks .
[FIGURE 5 OMITTED]
Voltage Fluctuation Caused by Wind Turbine
The wind turbine induction generator injects fluctuated active power into the grid and correspondingly it draws fluctuated reactive power from the grid.
Figure 6 shows a simplified diagram of wind turbine generator connected to grid. If the variation of the active power injected to the grid is [DELTA]P and the corresponding variation of the reactive power absorbed from the grid is [DELTA]Q, then voltage fluctuation, at PCC, [DELTA]V/V, is given in (7). The nominal voltage is 1 pu.
[DELTA]V/V [approximately equal to] [DELTA]P x R - [DELTA]Q x X (7)
which can be rewritten as follows;
[DELTA]V/V [approximately equal to][DELTA]S x Z x cos([theta] + ([phi]) (8)
R is the resistance of the grid impedance (pu);
X is the reactance of the grid impedance (pu);
[DELTA]S is the apparent power variation,
[DELTA]S = [square root of [P.sup.2] + [DELTA][Q.sup.2] (pu);
Z is the grid impedance amplitude (pu);
[theta] is the grid impedance angle; and
[phi] is [tan-.sup.1]([DELTA]Q/[DELTA]P).
[FIGURE 6 OMITTED]
Samples of Results of Wind Speed and Wind Turbine Modeling
Using the parameters of the wind turbine generator, which are given in the appendix, the wind speed and wind turbine models have been implemented under Matlab/Simulink. The wind turbine ratings are taken as base quantities. The grid fault level and X/R ratio are assumed 50 pu and 10 respectively. The no-load reactive power demand of the induction generator under study is compensated by capacitor banks installed at PCC. Figure 7 presents a sample of selected model outputs; equivalent wind speed, active/reactive power and voltage at PCC.
[FIGURE 7 OMITTED]
The wind speed variation, assuming turbulence intensity of 10%, and [U.sub.o] = 12 m/sec., is shown in Fig. 7(a). The corresponding aerodynamic power and electrical output power are shown in Fig. 7(b). Not all variations in the aerodynamic power are transmitted to the electrical power. It means that the soft shaft coupling and the inertia of wind turbine rotor and generator rotor masses damp and smooth the variations of the aerodynamic power. Figure 7(c) shows the variation of the absorbed reactive power from grid. It is clear that the voltage fluctuation, in Fig. 7(d), is very small due the high fault level of the grid.
Figure 8 traces the variation of the absorbed reactive power with the injected active power for the integrated wind energy system and the induction generator under study. The drawn reactive power increases with the increase of the generated active power. This relation is known as Q-P characteristic of the induction generator.
[FIGURE 8 OMITTED]
Influences of Grid Parameters on Flicker Caused by Wind Turbines
The grid parameters affecting the wind turbine flicker emission are the fault level, and X/R ratio of the gird impedance.
Figure 9 shows the variation of the short-term flicker index with different grid fault levels. This simulation test is carried out with two cases of grid impedance angles; 45[degrees] and 70[degrees]. The mean wind speed at hub level is maintained at 12 m/sec. and site turbulence is 10%. From Fig. 9, it can be seen that the flicker level decreases with the increase of fault levels.
[FIGURE 9 OMITTED]
XIR Ratio of grid impedance
The X/R ratio of the gird impedance is studied in terms of the impedance angle, [tan]=[tan.sup.-1](X/R). Figure 10 shows the variation of the short-term flicker index with the impedance angle. The fault level is maintained at 10 pu. The mean wind speed at hub level is 12 m/sec. and site turbulence is 10%.
From Fig. 6 it can be seen that the flicker decreases with the increase of [theta] untill the minimum point, then the slope is reversed and flicker increases with increase of [theta]. The 'V' curve trend for the relation of [P.sub.st] with the grid impedance angle agrees with those given in , . However, in , there is no indication to the minimum point and states that flicker increases with low X/R ratio.
The minimum point of voltage fluctuation is occurred when [theta] + [phi] = 90[degrees]. The angle [phi] can be obtained according to the incremental variation, [DELTA]Q/[DELTA]P, of Q-P characteristic of the induction generator (Fig. 8). The Q-P characteristic of the generator determines the [phi]-P relation. Then the mean generated power (operating point) determines the value of [phi] and consequently [theta]=90[degrees] - [psi]. at the point of minimum flicker emission.
Figure 11 shows the variation of angle [phi] with the active generated power. The mean active generated power is estimated accordance to the wind turbine power curve at mean wind speed. In this case, it is approximately 0.6 pu. as shown in Fig. 7(b). Then [phi] [approximately equal to] 8.6[degrees] which gives [theta] [approximately equal to] 81.4[degrees] at minimum flicker emission as shown in Fig. 10 The minimum point of flicker emission cannot be zero because the power swings up and down the mean value.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
Effects of Site Parameters on Wind Turbine Flicker Emission
The effects of mean wind speed and the site turbulence on flicker emission will be discussed.
Mean Wind Speed
The flicker severity is calculated for the same site turbulence ([I.sub.u] = 10%) and different mean wind speed, [U.sub.o]. The fault level of the grid is 10 pu. The [P.sub.st] values versus the mean wind speed are estimated for two grid impedance angles, 45[degrees]and 70[degrees].
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
The [P.sub.st] variation with the mean wind speed is illustrated in Fig. 12. It can be explained by the wind turbine power curve, shown in Fig. 13. From Fig. 13, it can concluded that the output power and its fluctuations in the low wind region are low and therefore the induced voltage fluctuation is small. As the wind speed increases from cut in speed to 13 m/sec., the output power fluctuations and [P.sub.st] increase, approximately in linear relation with the mean wind speed. However, in the stall region (greater than 13 m/sec.), the rate of change of the aerodynamic power curve is reduced, resulting in a corresponding reduction in the output electrical power variability. Then [P.sub.st] values vary in small range with the increase of the wind speed as shown in Fig. 12. The trend of [P.sub.st] versus the mean wind speed, shown in Fig. 12, agrees with this given in literature . However, in , , the flicker emission increases with increasing wind speed.
In this case, the mean wind speed at hub level is maintained at 12 m/sec., the fault level is 10 pu., and the grid impedance angle is 45[degrees]. Figure 14 shows the variation of [P.sub.st] with the turbulence intensity. The increase in the wind speed turbulence increases the power variability then the flicker emission increases with the increase of the turbulence intensity as shown in Fig. 14.
[FIGURE 14 OMITTED]
The comprehensive wind speed and wind turbine models can be applied for voltage fluctuation and power quality studies. The wind speed model involves the tower shadow and the rotational sampling of turbulence. A 2-mass drive train model, including soft shaft coupling, is used for damping and smoothing the output electrical power variations. A dq arbitrary reference frame is used for modeling of the asynchronous generator. The variations in the stator circuit are involved. The flicker level caused by voltage fluctuation is evaluated by the flickermeter, described in IEC 61000-4-15.
From simulation results, voltage fluctuations are widely affected by the grid strength and X/R ratio of grid internal impedance. The flicker emission is decreased with higher fault levels. The risk of voltage fluctuation increases in the resistive grids. The wind turbine operating point and the Q-P characteristic of the generator determine the point of minimum flicker emission. The trend of flicker variation with the mean wind speed depends mainly on the wind turbine power curve. The power variability and consequently flicker emission increases with turbulence increase. A wide look on the results indicates that grid parameters have more effect on flicker emission than site parameters.
The Wind Turbine Data, Drive Train Data and Generator Data are stated as follows:
--rated power 180 kW;
--hub height 30 m;
--rotor diameter 23.2 m;
--number of blades three;
--rotor speed 42 r/min;
--blade profile NACA-63 200;
--gearbox ratio 23.75.
--turbine inertia 102.8 [kg.m.sup.2];
--generator inertia 4.5 [kg.m.sup.2];
--stiffness of the shaft 2700 N.m/rad; (all data referred to the high speed shaft).
--nominal voltage 400 V;
--number of pole-pairs three;
--stator resistance 0.0092 Ohm;
--rotor resistance (referred to the stator) 0.0061 Ohm;
--stator leakage inductance 0.186 mH;
--rotor leakage inductance (referred to the stator) 0.427 mH;
--magnetizing inductance 6.7 mH.
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Hassan H. El-Tamaly *, Mohamed A. A. Wahab and Ali H. Kasem
Faculty of Engineering, EL-Minia University, EL-Minia 61111, EGYPT.
* Corresponding author. Address: Faculty of Engineering
EL-Minia University, EL-Minia 61111, EGYPT