Wind Turbine Flicker Calculation using Neural Networks

Wind Turbine Flicker Calculation using Neural Networks Stavros A. Papathanassiou

(1)

, Spyros J. Kiartzis

(2)

, Michael P. Papadopoulos

(1)

and Antonios G. Kladas

(1)

Electric Power Division, Dept. of Electrical & Computer Engineering, National Technical University of Athens 9, Iroon Polytechniou st., 15780 Zografou, Athens, GREECE. E-mail: [email protected]

(2)

Electric Energy Division, Dept. of Electrical & Computer Engineering, Aristotle University of Thessaloniki 54006 Thessaloniki, GREECE. E-mail: [email protected]

(1)

ABSTRACT The connection of wind turbines to the distribution networks may affect the voltage quality offered to the consumers. One of the factors contributing to this effect are the rapid variations of the wind turbine output power, which cause respective fluctuations in the supply voltage, referred to as flicker. This paper presents a neural network based model for wind turbine flicker emission calculations. Neural network training patterns are developed using a simulation model of a typical 500 kW stall-controlled wind turbine, by varying all wind and network parameters that might affect the expected flicker levels. The proposed neural network model predicts flicker emissions with sufficient accuracy under any normal operating conditions (wind speed mean value and turbulence intensity) and network characteristics (short circuit capacity, angle of Thevenin impedance and local load). The paper also includes an extensive discussion on the dependence of the flicker severity on the wind and network parameters considered. KEYWORDS: Wind Turbines, Flicker, Neural Networks

1. INTRODUCTION Wind Turbines (WTs) connected to electrical grids may affect the power quality of the supply, as a result of the fluctuating character of their output power. This contains both periodic components (due to aerodynamic phenomena, such as the tower shadow effect) and "random" variations (due to wind gusting and the general variability of the wind speed), resulting in corresponding fluctuations of the voltage magnitude along the feeder where the WTs are connected. Fluctuations in the frequency range between 0.5 and 35 Hz contribute to the light flickering effect, referred to as “flicker”. Flicker is evaluated according to the IEC 60868 standard [1,2]. A common measure of its severity is the short-term flicker index, Pst, measured over 10 min periods, whereas in certain cases (but not in WTs) the long-term (120 min) index, Plt, is also applicable. Wind turbine flicker emissions are receiving a lot of attention lately and standards are being developed to establish requirements and methods of assessment, (e.g. IEC 61400-21, [3]), which are generally based on measurements in existing installations. According to these standards, the WT manufacturers have to specify the continuous operation flicker coefficient, derived from a specific measurement procedure, as a function of the network impedance phase angle and the 10-min average of the wind speed. Flicker emission due to switching operations should be given as well. This information is then used to evaluate the expected flicker levels when the WT is connected to a specific point in the grid and examine the conformity with the applicable emission levels, as determined by national and international standards and recommendations (e.g. [4,5]). The importance of being able to predict the expected flicker emissions at the design stage or before the installation of a WT or wind farm is obvious. For this purpose, suitable WT and grid simulation models have been developed and applied, both in the time and frequency domain, e.g. as in [6-8].

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Neural networks are a promising area of artificial intelligence, having found numerous applications in modelling and forecasting applications in power engineering. A variety of neural network based models appeared in the last decade (e.g. [9,10]) and have been applied in many diverse areas, such as load forecasting, dynamic security assessment, component fault detection and diagnosis, machine control and parameter estimation. In this paper neural networks are applied to the calculation of the flicker induced by the operation of grid-connected wind turbines. The objective is to derive a single neural network which will predict flicker levels at the Point of Common Coupling (PCC) of the WT, under any normal operating conditions (wind speed mean value and turbulence intensity) and network characteristics (short circuit capacity, phase angle of Thevenin impedance and local load). These parameters will serve as inputs to the network, its output being the flicker severity index at the PCC. For this purpose, a set of training patterns (i.e. input-output combinations) of sufficient size and representativity is required. Although in principle the training set could be derived from an extensive measurement data-base, in practice such data are not available, particularly regarding the network characteristics (this would require measurements on the same WT, connected to a great variety of different network points). For this reason, the simulation model of a typical 500 kW stallcontrolled WT, presented in Section 2 of the paper, is used here for the creation of the training set. By varying all wind and network parameters that may affect the flicker levels, an extensive number of input combinations is generated. For each case the flicker severity index is calculated using the flickermeter algorithm of IEC 60868, outlined in Section 3. The neural network approach fundamentals and the application of this technique to the flicker calculation problem is presented in Section 4, followed by an extended discussion of the results obtained. Particular emphasis is placed on the investigation of the dependence of the flicker severity on the wind and network parameters. The developed neural network is “machine-specific”, since its generation is based on training patterns derived from simulations (or measurements, if data are available) on a specific WT. Once generated, the neural network permits the accurate and effortless computation of the expected flicker levels, without resorting to additional measurements or time-consuming simulations. The possibility, in particular, of substituting expensive and difficult to perform measurements is a very important aspect of the utility of the proposed neural network application and it is certainly worth investigating its applicability in simplifying extensive measurement campaigns, such as required in IEC 61400-21 ([3]).

2. STUDY CASE SYSTEM – MODELLING OF THE COMPONENTS 2.1 The Grid Eth=20 kV

∼

Zth

PCC

800 kVA 20/0.69 kV

500 kW WT

∼

Δ Υ AG XT=5% 200 CkVA SL=500 kVA cosφL = 0.8

3-Blade 29 rpm

Figure 1. Study case power system The study case power system considered in the paper is shown in Fig. 1. The medium voltage (MV) distribution grid is represented by its Thevenin equivalent, consisting of a voltage source Eth and the series impedance Zth. A concentrated local

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load is connected at the PCC, corresponding to the consumer loads in the nearby area. Although the local load could have been included in the Thevenin equivalent of the grid, it is modelled here independently in order to investigate its effect on the PCC voltage flicker. 2.2 The Wind Turbine The WT considered is a typical 500 kW stall-controlled unit. It is equipped with a squirrel cage induction generator, connected to the MV network via a 800 kVA, 0.69/20 kV step-up transformer. The 200 CkVA capacitor bank at the generator terminals provides no-load power factor correction The WT is equipped with a 3-blade fixed-pitch rotor, rotating at 29 rpm. The rotor aerodynamic characteristics are simulated using its static aerodynamic power coefficient, Cp(λ), curve, resulting in the power curve shown in Fig. 2.

600 500

Power (kW)

400 300 200 100 0

0

5

10 15 Wind speed (m/s)

20

25

Figure 2. Wind turbine power curve. In order to account for the aerodynamic torque pulsations at multiples of the rotor speed (the nP and 3nP harmonics, of a 3-blade rotor), a simplified representation of the tower shadow and wind shear effects is incorporated in the WT model. The effect of the tower is to reduce the aerodynamic torque of each blade as it sweeps in front of it. This is represented by an approximate reduction ΔVsh of the equivalent blade wind speed, in the 2θsh interval around the tower, as shown in Fig. 3. vw(δ) ΔVsh 2θsh

δ (rad) 0

3π/2-θsh 3π/2 3π/2+θsh

Figure 3. Tower shadow representation. The wind shear effect signifies the change of the horizontal wind speed component with the altitude, within the rotor disk area. As a result, the blades experience an increased equivalent wind speed at their top position (δ=π/2, in Fig. 3) and a reduced one at the bottom position (δ=3π/2). The wind shear is simulated by the widely used exponential law:

3

vw  z  =  vwh  zh 

α

(1)

where vw is the equivalent blade wind speed, acting on the aerodynamic centre of the blade, located at height z. vwh is the wind speed at the hub height, zh, and α the shear exponent. The variability of the aerodynamic torque, due to periodic variations, random wind speed fluctuations and gusting, is propagated in the drive train of the WT towards the output. The magnitude of the resulting output power fluctuations, and therefore the induced voltage flicker, depends critically on the torsional characteristics of the drive train, which must be properly represented in the simulation model. The mechanical equivalent utilised in this study is shown in Fig. 4 and consists of a number of lumped inertias, elastically coupled to each other, as it is common in WTs (e.g. [11,12]). The three inertias HB correspond to the three rotor blades. HH, HGB and HG represent the hub, gearbox and generator rotor, respectively, into which other secondary drive train elements are lumped (axes, disc brakes etc.). Cij and dij are the stiffness and damping coefficients of the elastic coupling between adjacent elements j and k. Dj is the external damping coefficient of the rotating inertia j. Inputs to the model are the generator torque TG and the aerodynamic torques TW1, TW2 and TW3, acting on each blade. TW1 ωB1, θB1

dHB CHGB ωGB, θGB CGBG ωG, θG

CHB CHB

DB TW2

DB HB

HB

HH dHB

ωB2, θB2

dHGB dHB

CHB DH

HGB

TG

HG DGB

dGBG

DG

HB ωB3, θB3

TW3

DB

Figure 4. Drive train 6-mass mechanical equivalent. The state equations of the drive train model are the following, expressed in per unit, using the base quantities of the Appendix: [0] [I ]   θ   [0]  d θ  ω  =  −[2H]−1[C] −[2H ]−1[D] ω  + [2H ]−1  T dt        

(2)

where θ = [θ B1 ,θ B 2 ,θ B 3 ,θ H ,θ GB ,θ G ]Τ

is the vector of the angular positions of the blades, hub, gearbox and generator Τ

ω = [ω B1 , ω B 2 , ω B 3 , ω H , ωGB , ωG ]

is the vector of the angular velocities of the blades, hub, gearbox and generator

T = [TW 1 , TW 2 , TW 3 , 0, 0, TG ]Τ

is the vector of the external torques, acting on the turbine blades (aerodynamic torques ΤW,j,

[0] and [I ]

j=1,2,3) and on the generator rotor (electromagnetic torque, ΤG, conventionally accelerating) are the 6x6 zero and identity matrices, respectively

[2H] = diag (2 H B , 2 H B , 2 H B , 2 H H , 2 H GB , 2 H G ) is the diagonal 6x6 inertia matrix

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0 0 0 0  −CHB  CHB  0 CHB −CHB 0 0 0    0 CHB 0 0 0  −CHB [C] =  C  0  −CHBG − HB −CHB −CHB CHGB + 3CHB  0 CHGB + CGBG −CGBG  0 0 −CHGB   CGBG  0 0 0 −CGBG  0

is the 6x6 stiffness matrix and

0 0 0 0  −dHB DB +dHB  0 D d d 0 0 0  + − B HB HB   0 DB +dHB 0 0 0  −dHB [D] =  d  is the 6x6 damping matrix 0  −dHB −dHB DH +dHGB +3dHB −dHBG  − HB  0 DGB +dHGB +dGBG −dGBG  0 0 −dHGB   DG +dGBG  0 0 0 −dGBG  0 For the induction generator, the well-known 4th order dq model is used, expressed in the arbitrary reference frame, rotating with an angular velocity ωdq (e.g. [13]): usd = −rs isd − ω dq Ψ sq + pΨ sd usq = −rs isq + ω dq Ψ sd + pΨ sq urd = 0 = r r ird − (ω dq − ω G ) Ψ rq + p Ψ rd

(3)

urq = 0 = r r irq + (ω dq − ω G )Ψ rd + p Ψ rq where p≡(1/ω0)(d/dt) and ω0 is the base electrical angular frequency. Generator convention is used for the stator currents. The stator and rotor fluxes are related to the currents by:

Ψ sd = − X s i sd + X m i rd Ψ rd = − X m i sd + X r i rd and Ψ sq = − X s i sq + X m i rq Ψ rq = − X m i sq + X r i rq

(4)

and the generator electromagnetic torque is given by TG = Ψ rd irq − Ψ rq ird = X m (isq ird − isd irq )

(5)

All variables in the above equations are expressed in per unit, using the base quantities defined in the Appendix. 2.3 The Wind

Figure 5. Generated wind speed time series. Average value 8 m/s, turbulence intensity 0.20. For the reproduction of suitable wind speed time-series, the Fourier synthesis method of [14] is employed, using the von Karman power spectral density function of the horizontal wind speed component. This method, frequently used in similar studies in the literature (e.g. [11,15]), provides a flexible tool for the generation of hub height wind speed time series of arbitrary length and sampling frequency, which otherwise might be unavailable from measurements. Input data are the average wind

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speed Vw and the turbulence intensity In. A sample time series generated by this method, for Vw=8 m/s and In=0.20, is shown in Fig. 5. Its length is 600 sec (10 min), which is the time interval required for the calculation of the short-term flicker severity index, Pst. In the case of wind turbines the normal operation long-term flicker coefficient, Plt, (based on 120-min time intervals) is equal to Pst and therefore requires no further examination.

3. FLICKER CALCULATION

u(t)

U

dB

dB

2

•

ΔU(t)

-3

-3 0

High Pass Filter

•

Hz

Hz 0.5

1

35

Low Pass Filter

pst(t)

2

Hz

Statistical Processing

Pst

8.8

Eye Response Curve

Brain Response (1st Order Lag)

Figure 6. UIE/IEC flickermeter functional diagram. The assessment of the short-term flicker severity index, Pst, is performed as specified in IEC 60868 and briefly described in this section, for the sake of completeness. Ιn Fig. 6, the UIE/IEC flickermeter block diagram is shown. Input is a 10-min time series of the voltage at the evaluation node, which may be expressed as u(t) = [U 0 + ∆U (t ) ]sin(ωt +ψ )

(6)

where U0 is the average node voltage magnitude, ΔU(t) the superimposed amplitude variations, ω=2πf the system frequency and ψ the initial phase angle. Using eqn. (6), the output of the first block of the flickermeter can be expressed as: u 2 (t) U 0 U  + ∆U (t ) −  0 + ∆U (t )  cos[2(ωt +ψ )] = U0 2  2 

The constant U0/2 in the above expression is eliminated by the high pass filter (1st order, 0.5 Hz cut-off frequency), whereas the double power frequency component is filtered out by the subsequent low-pass filter block (6th order Butterworth, 35 Hz cut-off frequency). Hence, output of the third block are the voltage magnitude variations, ΔU(t), in the frequency range 0.5 to 35 Hz. The next block in the diagram of Fig. 6 is a weighting function, simulating the perception ability of the human eye vs. the frequency of the disturbing signal. The peak of this curve is located at 8.8 Hz. Since the irritation caused is proportional to the square of the voltage magnitude fluctuations, the output of the weighting function block is squared and led to a 1st order lag (300 ms time constant), representing the memory tendency of the human brain. Its output is the time series of the instantaneous flicker sensation, pst(t). The calculation of the short term flicker index, Pst, requires then a simple statistical processing of the pst(t) time series. First the cumulative duration curve of the pst(t) values is found. The Pst index is then given by Pst = 0.0314 ⋅ P0.1s + 0.0525 ⋅ P1s + 0.0657 ⋅ P3s + 0.28 ⋅ P10 s + 0.08 ⋅ P50 s

(7)

where Px is the x % percentile (i.e. the flicker level which is exceeded for x % of the time), calculated from the pst(t) duration curve. The subscript “s” denotes smoothed values, obtained by averaging neighboring values of the duration curve, as described in IEC 60868-0.

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4. NEURAL NETWORK APPLICATION 4.1. The Concept of Neural Networks

X1

y

X2

y

f

Xn

Figure 7. The neuron. Neural networks provide alternative solutions to forecasting problems. Accuracy is the main advantage of neural networks, since they do not rely on human experience but are trained to learn the functional relationship between the system inputs and outputs. A neural network can be defined as a highly connected ensemble of processing elements called neurons. A neuron, schematically shown in Fig. 7, is a multi-input-single-output processing element consisting of a summation operation and an activation function. In a typical neuron the weighted sum of the inputs constitutes the argument of the activation function f, which determines the output value y and therefore the neuron characteristic. A type of activation function commonly employed is the sigmoid function, f(x) = [1+exp(-x)]-1, which monotonically maps the interval −∞ < x < ∞ into the interval 0 < f ( x) < 1 . The most frequently used sigmoid-type function, also employed in this paper, is the hyperbolic tangent, which is non-linear, permitting training of the network to capture the non-linearities of complex systems: x

−

x

 x  e2 − e 2 f ( x) = tanh   = x x − 2 e2 + e 2

∈ ( −1,1)

(8)

Fig. 8 illustrates the architecture of a typical neural network, which consists of an input layer, one hidden layer and an output layer. Neurons in a layer are generally interconnected to all neurons in the adjacent layers with different weights. Each neuron receives its inputs from neurons in the higher layer through interconnections and propagates its activation to the neurons in the next lower layer, (e.g. [16]). Notably, input layer neurons lack the activation function processing of the subsequent layers, their role being to receive and propagate the input values to the neurons of the first hidden layer.

1 = x0

1 = y0

{ wi0(1)}

x1

Ó

y1

x2

Ó

y2

xn

Ó

yp

Input layer

{

wij(1)}

f

f

f

(2) { wk0 }

y1

y2

yp

{ Hidden layer

(2) wki }

Ó

o1

Ó

o1

Ó

o1

f

o1

f

o2

f

om

Output layer

Figure 8. Neural network architecture.

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A neural network can be trained to learn the functional relationship between its inputs and its outputs as follows: The neural network is presented with a set of Q input-desired output training data {xq, dq, q=1,...,Q}, also called training patterns. Inputs {x1, x2, ..., xQ} are applied to the input layer. The neural network is trained to respond to the corresponding desired output vectors {d1, d2, ... dQ}. The training continues until the average error between the desired and the actual outputs over the Q training patterns is less than a predefined threshold. The minimisation of the output error is achieved through a gradient algorithm. The Generalised Delta Rule (GDR) ([17]) is used in this paper. Initially, the neural network weights are given small random numbers. When the neural network is presented with a training pattern {xq, dq} the input signal, xq, is propagated in the forward direction in the network in order to compute the output oq and error eq = dq - oq. Then, the error, eq, is propagated through the network in the backward direction for the computation of the gradients of the error with respect to the network weights. Because of this backward propagation of the error, the GDR is also called error back-propagation algorithm. The objective of the neural network training is to minimise the average error over all training patterns: J=

T 1 Q 1 Q 1 Q dq − oq ) ( dq − oq ) = ∑ J q (eq )T e q = ( ∑ ∑ Q q =1 Q q =1 2Q q =1

(9)

where J q = (e q )T e q .

4.2. Neural Network Model for Flicker Calculation A prerequisite for the generation of neural networks capable of predicting with sufficient accuracy the expected flicker levels is the identification of the physical parameters that might affect the flicker emissions of a given wind turbine. These parameters will be candidate inputs to the neural network to be created. Subsequently, a set of input-output combinations is generated and used for the training of the neural network. Each element of the training set comprises the values of the input parameters for the specific operating conditions, and the resulting flicker emission, as expressed by the flicker severity index, Pst. To ensure the ability of the developed neural network to correctly calculate the flicker severity under all possible (and realistic) wind and network conditions, the cases included in the training set should span the entire expected range of variation of the input parameters. It is known that the output power variability of a wind turbine is strongly affected by the average wind speed, Vw, and the turbulence intensity, In. The voltage fluctuations, resulting from the variability of the WT output power, are then determined by the Thevenin impedance, Z!th , of the network at the PCC. Thus, two additional parameters of interest are the short circuit capacity at the PCC, Ssc, and the angle φth = arctan ( X th Rth ) of the complex impedance Z!th . Another factor that might affect the PCC voltage flicker is the local load level, SL. The range of variation considered for each of these five input parameters is shown in Table 1. Scanning the range of each parameter, a training set is created which spans all possible wind and network conditions. For each combination, the wind turbine operation is simulated for a 10-min interval, using wind speed time series generated as described in Section 2.3. Then, the UIE/IEC flickermeter algorithm, outlined in Section 3, is applied to obtain the resulting short-term flicker severity index, Pst. The majority of the input-output patterns thus generated are used for training purposes, while the remaining cases are utilised as an independent test set, for evaluating the neural network performance in unforeseen (i.e. not included in the training set) operating conditions.

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Input parameter

Range of variation

1. Mean wind speed, Vw

4 - 20 m/s

2. Turbulence intensity, In

0.02 – 0.3

3. Grid short circuit capacity at the PCC, Ssc

5 – 50 MVA

4. Angle of Thevenin impedance at the PCC, φth

10 – 90 deg

5. Local load, SL

100 – 1000 kVA

Table 1. Wind and network parameters considered and respective range of variation. Various tests were performed in order to identify the “optimum” number of hidden neurons and layers of the proposed neural network model. The selection criteria were both the minimisation of the training error and the time required. This procedure led to the fully connected 4-layer feed-forward neural network, shown in Fig. 9, which has 5 input neurons, 4 neurons in the first and 3 neurons in the second hidden layer and 1 output neuron, providing the forecasted value of Pst. The five input neurons represent the mean wind speed Vw, the turbulence intensity In, the network short circuit capacity Ssc, the angle φth and the load level, SL, at the PCC. It was found that the selection of the training data set significantly affects the performance of the model. Many experiments were conducted in order to identify a selection of the training patterns that gives the best results at a reasonable training time. Too large a training set would comprise obsolete data and require high training times. The training data set eventually selected consists of 680 input/output training patterns. Using the back-propagation algorithm, the network was trained until the average error became less than 4%. It was observed that further training did not improve the accuracy of the forecasts, since training of the neural network to a very small error, results in data over-fitting. Once trained, the network parameters are kept fixed and flicker forecasts are obtained, as discussed in detail in the following section.

Vw In Ssc

Pst

φth SL

Figure 9. Neural network model for flicker forecasting. 4.3 Neural Network Testing Results In this section, the performance of the developed neural network is investigated in predicting the flicker levels and their

9

dependence on the wind and network parameters considered. For this purpose, the neural network results are compared to the calculated flicker index values for a variety of test cases, not included in the neural network training set. Each time, one parameter is varied, while the others remain fixed at their “base case” values, which are the following: • Mean wind speed, Vw=10 m/s • Turbulence intensity, In=0.10 • Network short circuit capacity, Ssc=10 MVA (20 times the WT rated power) • Network impedance ratio Rth/Xth=0.6 (φth≈60o) • PCC Load: SL=500 kVA, cosφL=0.8 lag. In Figs. 10 and 11 the results of the neural network are compared with the calculated flicker index values for varying network short circuit capacity and impedance angle at the PCC. In Fig. 12 the flicker values (calculated and forecasted) are plotted against the average wind speed, for three different network impedance angles, and in Fig. 13 as a function of the wind turbulence intensity. The effect of the aggregate system load at the PCC is illustrated in Fig. 14.

0.10 Calculated 0.08

Forecasted

Pst

0.06 0.04 0.02 0.00 0

10

20

30

40

50

60

Ssc [MVA]

Figure 10. Neural network performance in predicting the variation of Pst with the network short circuit capacity, Ssc

0.35 Calculated

0.30

Forecasted

Pst

0.25 0.20 0.15 0.10 0.05 0.00 0

15

30

45

60

75

90

arctan(X/R) [deg]

Figure 11. Neural network performance in predicting the variation of Pst with the network angle, φth=arctan(Xth/Rth).

10

R th/Xth=0.6 0.07 0.06

Pst

0.05 0.04 0.03 0.02

Calculated

0.01

Forecasted

0.00 0

5

10

15

20

V w [m/s]

R th/Xth=0.8 0.12 Calculated

0.10

Forecas ted

Pst

0.08 0.06 0.04 0.02 0.00 0

5

10

15

20

Vw [m/s]

R th/X th=1.0 0.16 0.14 Calculated

0.12

Forecasted

P st

0.10 0.08 0.06 0.04 0.02 0.00 0

5

10

15

20

V w [m/s]

Figure 12. Neural network performance in predicting the variation of Pst with the mean wind speed, for three network impedance angles (Rth/Xth=0.6, 0.8, 1.0).

0.200 0.175 0.150 Pst

0.125 0.100 0.075 0.050

Calculated

0.025

Forecasted

0.000 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

In

Figure 13. Neural network performance in predicting the variation of Pst with the wind turbulence intensity, In.

11

0.065 Calculated 0.060

Forecasted

Pst

0.055 0.050 0.045 0.040 0

200

400

600

800

1000

1200

Load [KVA]

Figure 14. Neural network performance in predicting the variation of Pst with the local load, SL.

Observing these diagrams, the neural network capability of forecasting reliably the WT flicker emission is fully confirmed. The output of the neural network tracks very closely the actual (i.e. calculated from the simulation results) flicker variation curves, with consistent error behaviour in all cases. In Table 2 the mean and maximum forecast errors are summarised, for each diagram of Figs. 10 to 14. All error values appearing (mean and maximum) are perfectly acceptable, since even a 10% error cannot be regarded as unacceptably high when evaluating a stochastically varying quantity such as flicker.

Flicker parameter

Mean forecast error (%)

Maximum forecast error (%)

Pst=f(Vw), Rth/Xth=0.6

5.816

7.506

Pst=f(Vw), Rth/Xth =0.8

4.269

7.086

Pst=f(Vw), Rth/Xth =1.0

1.767

3.181

Pst=f(In)

3.202

6.240

Pst=f(Ssc)

5.336

8.945

Pst=f(φth)

6.132

8.617

Pst=f(SL)

0.485

0.903

Table 2. Mean and maximum forecast error per flicker parameter. 5. DISCUSSION The neural network testing results presented in the previous section, besides providing the neural network forecasting accuracy and its sensitivity to the various parameters considered, contribute also to the better understanding of the physical relation between the induced flicker and the wind and system characteristics. This is examined in more detail in the following. In Fig. 10, the inversely proportional relation between Pst and the short circuit capacity of the feeding network is clearly apparent. This is a well-known and rather obvious fact, incorporated in all flicker evaluation recommendations (e.g. [3,5]), since

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a given variability of the WT output power will result in higher voltage flicker in case of a weak (low Ssc) grid. This is also justified by eqn. (10), presented in the following. The V-shaped curve of Fig. 11 can be explained using the following simplified relation, associating power and voltage variations (all quantities in per unit): ∆S (10) cos (φth + φ ) S sc where ΔU is the PCC voltage change, due to a change ΔP and ΔQ in the active and reactive power flowing into the system. By ∆U ≈ Rth ∆P − X th ∆Q ⇒ ∆U ≈

convention, active power is positive when exported to the infinite system and reactive when drawn from the system. ΔS is the corresponding apparent power change and φ is given by  ∆Q  (11) φ = arctan    ∆P  For a WT equipped with a grid connected induction generator, an increase in the produced active power (ΔP>0) is always accompanied by an increase in the reactive power drawn by the generator (ΔQ>0), hence φ>0. The angle φ is the slope of the induction generator P-Q curve and should not be confused with the power factor angle, φPF=arctan(Q/P).

500

Q (KVAr)

400

300

200

100

0

0

100

200

300 P (kW)

400

500

600

Figure 15. P-Q curve of the study case induction generator. 90 80 70

Angle (deg)

60 50

φPF

40 30 φ

20 10 0

0

100

200

300 P (kW)

400

500

600

Figure 16. Diagram of angles φ and φPF for the study case induction generator.

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The P-Q curve of the induction generator considered in this study is shown in Fig. 15 and the respective diagram of angles φ and φPF in Fig. 16, as a function of the generator active power (for operation at rated voltage). At the “base case” 10 m/s wind speed, the WT power is approx. 330 kW and φ≈25o, as it is found from Figs. 2 and 16. Hence, from eqn. (10) it is deduced that minimum flicker emissions would occur at a network impedance angle φth≈65o, where φth+φ=90o. Deviating from this angle, the voltage fluctuations and therefore the flicker increase, which fully explains the shape of the Pst curve in Fig. 11. Eqn. (10) also justifies the inversely proportional relation between Pst and Ssc, observed in Fig. 10. The Pst variation with the mean wind speed Vw, illustrated in the diagrams of Fig. 12, can be explained considering first the power curve of the simulated WT, shown in Fig. 2. In the low wind region the output power is low and therefore the induced voltage fluctuations not significant. As the wind speed increases, the output power fluctuations and hence Pst also increase, approximately in proportion to Vw. However, the slope of the WT power curve beyond 12-13 m/s is drastically reduced, resulting in a corresponding reduction in the output power variability. The other important factor affecting the shape of these diagrams and the position of their peaks is the change in the WT operating point, and thus of φth+φ in eqn. (10), with the wind speed. More specifically, as Vw exceeds 9-10 m/s, φth+φ approaches 90o and for this reason the flicker index starts reducing well before the knee-point of the WT power curve. The “irregularity” of the Rth/Xth=0.6 (φth≈65o) diagram (Fig. 12) between 9 and 13 m/s is also due to the angle φth+φ transversing the 90o region. This is not observed in the other two diagrams of Fig. 12 (φth≈50o and 45o) because the maximum value of φ in Fig. 16 is 40o and thus φth+φ cannot exceed 90o. At this point it must be noted that the simplified aerodynamic model used in the paper is inappropriate for representing dynamic stall phenomena. In practice, the output power of a stall regulated WT exhibits a much higher variability above rated wind speed, increasing considerably its flicker emission. Thus, the decline of Pst observed in Fig. 12 around and beyond the rated wind speed is rather optimistic. Using more elaborate aerodynamic models to represent the torque and power variability in the high wind region is possible but would increase dramatically the computation time for generating the training set. However, once this was achieved, the developed neural network would reliably predict flicker in this region of wind speeds, obviating the need for time-consuming simulations. It is also worth investigating the combined use of measurement data and simulations for the creation of the training set. The almost linear relation between Pst and the turbulence intensity In, evident in Fig. 13, is expected, since high wind turbulence indicates a correspondingly high variability of the output power. The local load connected at the PCC has been simulated as a static load, represented by a constant impedance. Hence, its effect is to increase slightly the fault level of the system, being connected in parallel to the Thevenin impedance, Zth. For this reason, increasing load levels result in a small reduction of the flicker intensity, as shown in Fig. 14. The load power factor also plays a certain role, affecting the angle of the resulting system impedance, Zth//ZL, but not critically. More important may be the load type, i.e. dynamic (motor) load instead of static. Significantly reduced flicker levels are reported in [7] when motor load is connected to the system. Investigations conducted by the authors and presented in [6] have shown that representing the PCC load as dynamic (induction motor, modelled by the standard 3rd order “transient” equivalent) results in modified Pst values, but to a much smaller extent and not necessarily reduced. Nevertheless, this is a point that requires further investigation, if more general conclusions are sought. 6. CONCLUSIONS An application of neural network theory in the assessment of the flicker emission by grid connected wind turbines has been presented in this paper. A comprehensive WT model was employed to simulate the operation of the machine against a study

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case infinite system, as described in Section 2. Using this model, a set of training patterns was generated, by varying the wind and network parameters, which might affect the flicker induced by the operation of the WT. These parameters are the average wind speed and the turbulence intensity, the short circuit capacity and Thevenin impedance angle of the network and the local load level. Using the training data, a neural network model was developed which is capable of predicting flicker emissions with sufficient accuracy under any normal operating conditions and network characteristics. The neural network was comprehensively tested and all error indices (mean and maximum) were perfectly acceptable. The neural network results track very closely the actual flicker variation curves, with consistent error behaviour in all cases. Along with the neural network testing results, a detailed investigation was also presented of the dependence of the induced flicker on the wind and network parameters considered.

7. ACKNOWLEDGEMENT Part of the work presented in this paper has been conducted within the EU project “Integration of Wind Turbines into Electricity Supply Networks with Limited Power Transportation Capacity – WIRING” (JOR3-CT98-0245). The authors gratefully acknowledge the support of the European Commission in their efforts.

8. NOMENCLATURE Eth

Internal EMF of network Thevenin equivalent

Z!th = Zth∠φth = Rth + jXth Impedance (magnitude ∠ angle and resistive-reactive part) of the network Thevenin equivalent Ssc

Network short-circuit capacity at the PCC

SL

Consumer load at the PCC

rs, rr

Induction generator stator and rotor resistance

Xs, Xr

Induction generator stator and rotor reactance

Xm

Induction generator magnetising reactance

usd, usq

d and q components of induction generator stator voltage

isd, isd, ird, ird

d and q components of induction generator stator and rotor current

Ψsd, Ψsq

d and q components of induction generator stator flux

Ψrd, Ψrq

d and q components of induction generator rotor flux

ωdq

Angular velocity of the arbitrary dq reference frame

ω0

Base electrical angular velocity

p≡(1/ω0)(d/dt)

Derivation operator

Cp

Rotor aerodynamic power coefficient

λ

Tip speed ratio

vw

Wind speed

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vwh

Wind speed at hub height

zh

Hub height

a

Wind shear exponent

ΔVsh

Equivalent wind speed reduction due to tower shadow

θsh

Tower shadow angle

Hk

Inertia constant of rotating mass k (k=B1,B2,B3,H,GB,G)1

Dk

External damping coefficient of rotating mass k (k=B1,B2,B3,H,GB,G)1

Cjk

Stiffness coefficient of coupling between adjacent inertias j and k (j,k=B1,B2,B3,H,GB,G)1

djk

Relative damping coefficient of coupling between adjacent inertias j and k (j,k=B1,B2,B3,H,GB,G)1

θk

Angular position of rotating mass k (k=B1,B2,B3,H,GB,G)1

ωk

Angular velocity of rotating mass k (k=B1,B2,B3,H,GB,G)1

TG

Generator electromagnetic torque

TWj

Aerodynamic torque acting on blade j (j=1,2,3)

Vw

10-min average wind speed

In

Turbulence intensity

u(t)

Instantaneous node voltage

U0

10-min average voltage magnitude

ΔU

Voltage magnitude change

ω

System frequency (ω=2πf)

ψ

Initial phase angle of the node voltage

pst(t)

Instantaneous flicker severity index

Px

x % percentile of the instantaneous flicker, pst(t)

Pst

Short-term (10 min) flicker severity index

Plt

Long-term (120 min) flicker severity index

ΔP,ΔQ,ΔS

Change in active, reactive and apparent power exported to the grid

φ=arctan(ΔQ/ΔP)

Angle of incremental change in output power

φPF

Induction generator power factor angle

q

x

dq o

q

Neural network input training data Neural network desired output training data Neural network output

eq

Neural network forecast error

J

Neural network average forecast error

Q

Number of neural network training patterns

Wij

Neural network weights

1

Bj: Blade j (j=1,2,3), H: Hub, GB: Gearbox, G: Generator

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9. REFERENCES [1] IEC 60868 “Flickermeter - Functional and design specifications”, 1st Edition, 1986 and Amendement 1, 1990. [2] IEC 60868-0 “Evaluation of flicker severity”, 1991. [3] IEC 61400-21 “Measurements and assessment of power quality characteristics of grid connected Wind Turbines (WT)”. Final Draft, 1999. [4] IEC 61000-3-7, “Assessment of emission limits for fluctuating loads in MV and HV power systems”, 1996. [5] VDEW, “Eigenerzeugungsanlagen am Mittelspannungsnetz”, 1994 (revised 1998). [6] Papadopoulos MP, Papathanassiou SA, Tentzerakis ST and Boulaxis NG (1998), “Investigation of the Flicker Emission by Grid Connected Wind Turbines”. Proc. of 8th IEEE Int. Conf. on Harmonics and Quality of Power, Athens, pp. 1152-1157. [7] Saad-Saoud Z and Jenkins N (1999), “Models for Predicting Flicker Induced by Large Wind Turbines”. IEEE Trans. Energy Conversion, Vol.14, No.3, pp. 743-748. [8] Amaris H, Vilar C, Usaola J and Rodriguez JL (1998), “Frequency Domain Analysis of Flicker Produced by Wind Energy Conversion Systems”. Proc. of 8th IEEE Int. Conf. on Harmonics and Quality of Power, Athens, pp. 1162-1167. [9] D. Niebur et al. (1995), “Artificial neural networks for Power Systems”. CIGRE TF38.06.06 Report, ELECTRA, No. 159, pp. 77-101. [10] M. El-Sharkawi and D. Niebur (editors) (1996), “A Tutorial Course on Artificial Neural Networks with Applications to Power Systems”, IEEE/Power Engineering Society, 96TP112-0. [11] Wasynzuk O, Man DT and Sullivan JP (1981), “Dynamic Behavior of a Class of Wind Turbine Generators during Random Wind Fluctuations”. IEEE Trans. Power Apparatus and Systems, Vol. 100, No.6. [12] Chedid R, LaWhite N and Ilic M (1993), “A Comparative Analysis of Dynamic Models for Performance Calculation of Grid-Connected Wind Turbine Generators”. Wind Engineering, Vol. 17, No. 4. [13] Krause PC (1986), Analysis of Electric Machinery, McGraw-Hill. [14] Shinozuka M and Jan CM (1972), “Digital Simulation of Random Processes and Its Applications”. Journal of Sound and Vibration, Vol.25, Nov. 1972, pp. 111-128. [15] Chan SM, Cresap RL, Curtice DM (1984), "Wind Turbine Cluster Model". IEEE Trans. Power Apparatus and Systems, Vol. 103, No.7. [16] Mohammed O, Park DC, Uler FG and Ziqiang C (1992), “Design Optimization of Electromagnetic Devices using Artificial Neural Networks”, IEEE Trans. on Magnetics, Vol. 28, No. 5. [17] Pao Y-H (1989), Adaptive Pattern Recognition and Neural Networks, Addison-Wesley Inc.

APPENDIX

Mechanical base quantities The base quantities used for per-unitizing the equations of the drive train mechanical equivalent are given in this section. If SB is the base power (VA), ω0 the base electrical angular velocity (rad/sec) and Ρ the number of poles of the generator, then the base values at the high-speed (generator) side of the drive train are defined as follows:

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ω B′ = TB′ =

ω0 P/2

the base mechanical speed, in mechanical rad/sec

SB ω B′

the base torque, in Nm

θ B′ ≡ ω B′

the base mechanical angle, in mechanical rad/sec

J B′ =

SB TB′ = 2 ′ 0.5ω B 0.5ω B′

the base inertia, in Nm/(rad/sec)

CB′ =

TB′ S = B2 ′ ω B ω B′

the base stiffness coefficient, in Nm/(rad/sec)

DB′ ≡ d B′ =

TB′ S = B2 ′ ω B ω B′

the base damping coefficient, in Nm/(rad/sec)

In the above equations, the prime denotes high-speed side values. The low-speed (rotor) side base quantities are then found using the following relations:

ω B′ = n ω B′′

J B′′ = n 2 J B′

ϑB′ = n θ B′′

DB′′ = n 2 DB′

TB′′ = n TB′

CB′′ = n 2 CB′

where n is the gearbox transfer ratio and the double-prime denotes low speed side values.

Electrical base quantities The rms base current I Babc is found from the base power SB and the rms base voltage VBabc (phase-to-neutral): I Babc =

SB 3VBabc

where the subscript «abc» denotes abc system values (as opposed to dq). The base impedance is defined as: Z Babc =

2 VBabc 3VBabc = I Babc SB

The dq system base voltage and current are equal to the respective abc instantaneous base values: VBdq = 2VBabc

I Bdq = 2 I Babc

Using these definitions, the base power SB is then given by 3 S B = VBdq I Bdq 2 The dq base impedance is equal to the respective abc value VBdq Z Bdq = = Z Babc I Bdq

AUTHOR BIOGRAPHIES Stavros A. Papathanassiou was born in Thesprotiko, Greece, in 1968. He received the Diploma in Electrical Engineering from the National Technical University of Athens (NTUA), Greece, in 1991 and the Ph.D. degree in 1997 from the same University. His research mainly deals with electric machines and drives, wind turbine modelling and control and the analysis of autonomous power systems with large wind penetration. He is a member of the IEEE Power Engineering, Industry Applications and Power Electronics Societies and a registered professional engineer and member of the Technical Chamber of Greece.

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Spyros J. Kiartzis was born in Thessaloniki, Greece, in January 1969. A graduate of the Aristotle University of Thessaloniki, he studied electrical and computer engineering (Dipl. EE ’92, Ph.D. ’98). Upon completion of his military service in the Greek Army in the Engineering Command Headquarters he returned to the Aristotle University of Thessaloniki in 1998 as a researcher. His research interests are in artificial intelligence applications, in power systems and in electric machines and drives. Dr. Kiartzis is a member of IEEE, CIGRE, the New York Academy of Sciences and the Society of Professional Engineers of Greece. Michael P. Papadopoulos was born in Ioannina, Greece, in 1932. He received the Diploma in Electrical and Mechanical Engineering in 1956 and the Ph.D. degree in 1974 from the National Technical University of Athens (NTUA), Greece. In 1956 he joined the Public Power Corporation of Greece, where he was engaged in the planning, design, operation and control of rural and urban distribution networks, as well as in the utilisation of electric energy. He is currently Professor in the Department of Electrical and Computer Engineering of NTUA. His research interests lie in the field of distribution systems and renewable energy sources. He is a member of the IEEE Power Engineering Society and a registered professional engineer and member of the Technical Chamber of Greece. Antonios G. Kladas was born in Athens, Greece, in 1959. He received the Diploma in Electrical Engineering from the Aristotle University of Thessaloniki, Greece in 1982 and the DEA and Ph.D. degrees in 1983 and 1987 respectively from the University of Pierre and Marie Curie (Paris 6), France. He served as Associate Assistant in the University of Pierre and Marie Curie from 1984-1989. During the period 1991-1996 he joined the Public Power Corporation of Greece, where he was engaged in the System Studies Department. Since 1996 he is Assistant Professor in the Department of Electrical and Computer Engineering of the National Technical University of Athens (NTUA). His research interests include electric machine modelling in generating units by renewable energy sources and industrial drives.

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