Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 116.

55

Performance Enhancement of Grid Connected Wind Energy Conversion Systems

J. Ravishankar and M.F. Rahman School of Electrical Engineering & Telecommunications

University of New South Wales Sydney, NSW 2052, Australia

{jayashri.ravishankar & f.rahman}@unsw.edu.au Abstract - The aim of this paper is to enhance the steady state and dynamic performance of grid connected Wind Energy Conversion Systems (WECSs) in India. The WECS considered is a fixed-speed system that is equipped with a squirrel-cage induction generator. The drive-train is represented as a two-mass model. A wind farm consisting of ten wind turbines is considered for analysis. The total capacity of the wind farm is 7.5 MW. In this paper, the steady state performance of the WECS is analyzed using a simultaneous method of power flow algorithm. Simulation results using various types of compensation reveal that a combination of series and shunt compensation improves the overall steady state performance of the system. The dynamic performance of grid connected WECS is analyzed in terms of rotor speed stability. The enhancement of dynamic performance is explored with a Unified Power Flow Controller (UPFC) connected at the Point of Common Coupling (PCC). The gains of the UPFC are tuned using a simple Genetic Algorithm (GA). It is observed that the UPFC, which is a series-shunt controller, helps not only in regulating the voltage, but also in mitigating the rotor speed instability. Index Terms - Wind energy; reactive power compensation; power flow; rotor speed stability; UPFC;

I. INTRODUCTION

One of the most critical issues for the development of wind energy in India has been the transmission capacity of the grid in the areas where the wind farms exist. Wind farms are concentrated in the rural areas where the existing transmission grids are very weak. Most of the electric machines used with the wind turbines in India, are of fixed-speed type equipped with squirrel-cage induction generators. In addition, the wind farms were developed during a comparatively short period of time in a few areas, and the reinforcement of the transmission systems in these areas has lagged behind the fast development of wind energy [1]. In case of fixed-speed wind turbines, reactive power support is needed at wind energy conversion system (WECS) terminals for voltage regulation and improvement of low voltage ride-through capabilities. As the wind speed continuously changes, the voltage at the point of common coupling (PCC) fluctuates. A possible way to improve this situation is by incorporating reactive power compensation. In this paper, the power flow of a radial system with WECS is simulated, using a simultaneous method of power flow. Simulation results show that the series-shunt

compensation results in a very good voltage profile at PCC and a significant reduction in transmission line current due to the reduction of reactive power flow through the line. This also allows more turbines to be connected at the PCC. When fault occurs, the voltage at the WECS terminals drops. Thus the generated active power falls, while the mechanical power does not change and so the induction generator accelerates. After fault clearance, the reactive power consumption increases, resulting in reduced voltages near the generating unit. Thus the induction generator voltage does not recover immediately after fault, but a transient period follows. As a consequence, the generator continues to accelerate, and this may lead to rotor speed instability [2]. Thus, it is clear that the dynamic controller used should not only provide the needed reactive power support for voltage regulation but should also help to damp out the rotor speed oscillations.

II. MODELLING OF WECS

Fig. 1 shows the schematic diagram of a typical WECS. A description of sub-models (or components) is presented in the following sections.

Fig. 1 Schematic diagram of a typical WECS

A. Wind Turbine Model The simple aerodynamic model commonly used to represent the turbine is based on power performance versus tip-speed ratio. The power extracted from the wind turbine is given by [3],

,21 3υρ Pw aCP = (1)

where ρ is the density of dry air, a is the swept area of the blades in m2, CP is the power coefficient and υ is the velocity of the wind in m/s. A general expression for CP is given in [4].

56

B. Drive-Train Model In case of conventional WECS models, accurate results are

obtained by increasing the number of masses, springs and damper which are used to represent the physical characteristics of the actual system. It has been proved that the two-mass model for WECS representation is fairly accurate [5]. Thus this approach is adopted here and is shown in Fig. 2, where the wind turbine and the generator rotor are modelled as two masses and the wind mill shafts as spring element.

Fig. 2 The simplified two-mass model

The dynamic equations of the two-mass representation

are given by [6],

),(2

,2

,2

et

e

ee

t

tt

fdtd

HTK

dtd

HKT

dtd

ωωπδ

δω

δω

−=

−=

−=

(2)

where T is the torque, δ is the angular displacement between the two ends of the shaft, ω is the angular speed, H is the inertia constant and K is shaft stiffness. The subscripts t and e stand for wind turbine and generator parameters, respectively.

C. Electric Generator The generator model considered here is a squirrel-cage

induction generator driven by a wind turbine with fixed blades, i.e. a stall-regulated fixed-speed turbine. The induction generator is directly connected to the grid. In the operating region, the rotor speed varies within a very small range of slip (around 1 to 5% of the synchronous speed). This has negligible aerodynamic effect and hence, these are considered fixed speed generators.

The steady state model of such an induction machine is represented by the well known equivalent circuit [7]. The equation for the air gap power is,

,12

22 s

sRIPg−

−= (3)

where I2 is the rotor current, R2 is the rotor resistance and s is the slip. For the dynamic analysis, the differential equations of the induction generator contains only fundamental frequency components and the stator flux linkage transients are neglected. The equations are then given by [7],

[ ] ,)(1 ''''

0

'

qqsssdd sVIXXV

TdtdV

+−+= (4)

[ ] ,)(1 ''''

0

'

ddsssqq sVIXXV

TdtdV

+−+= (5)

where V’ is the voltage behind transient reactance, Is is the stator current, T0’ is the open circuit time constant, Xs is the stator reactance and Xs’ is the transient reactance of the machine. The subscripts d and q stand for the direct and quadrature axis values, respectively. The swing equations have been included in the mechanical model given by (2). The electromagnetic torque, Te, is computed as, .''

qsqdsde IVIVT += (6)

III. STEADY STATE ANALYSIS The power flow analysis with the WECS is quite

complicated, unlike the analysis with conventional sources, because,

• The power injected into the grid by WECS depends on the instantaneous wind speed, which varies unpredictably.

• With the use of squirrel-cage induction generators, the operating slip of the machine has to be determined. The machine operates at a slip for which the mechanical power developed by the turbine is equal to the electrical power developed by the induction generator.

In this paper, the power flow analysis is carried out using a simultaneous method [8]. This method determines simultaneously the state variables corresponding to nodal voltage magnitudes and angles of the network and slip of induction generators. In this method, the WECS is modelled as a variable PQ bus. Assuming adequate initial conditions, the method retains Newton’s quadratic convergence. Here, the Newton-Raphson power flow algorithm is reformulated to include the mismatch equation ΔPm (difference between the power extracted from the turbine and electrical power developed in the machine). The unified power flow formulation is,

[ ] ,

][

][

x

][

][

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

Δ

⎥⎥⎦

⎤

⎢⎢⎣

⎡Δ

Δ

⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎦⎤

⎢⎣⎡

∂Δ∂

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂Δ∂

−⎥⎦⎤

⎢⎣⎡

∂Δ∂

−

⎥⎦⎤

⎢⎣⎡∂∂

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎥⎦⎤

⎢⎣⎡∂∂

⎥⎦⎤

⎢⎣⎡∂∂

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂∂

⎥⎦⎤

⎢⎣⎡∂∂

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

Δ

Δ

Δ

s

VV

sP

VPVP

sQ

VQVQ

sP

VPVP

P

Q

P

mmmm

θ

θ

θ

θ

(7)

where ⎥⎦

⎤⎢⎣

⎡∂Δ∂

sPm is a diagonal matrix whose order is equal to the

number of wind farms in the network. Their elements are given by,

),(/][21

21123 6 CB

sCAe

DrCECCa

sP Cm −+−=∂Δ∂ Λυωυρ (8)

where the expressions for A to E, and Λ are given in the Appendix and C1, C2 and C6 are constants in the power coefficient equation [4].

57

The power flow is carried out on a 9-bus radial system given in Fig. 3 [3]. Ten wind turbines are assumed to be connected at the PCC (bus 9).

Fig. 3 Single line diagram of 9-bus radial system

The reactive power compensation for WECS is

traditionally done with capacitor banks, which is an economic and relatively simple solution. In shunt compensation, the capacitor is used to compensate the individual induction generators. In series compensation, the capacitor is used to compensate the line impedance. Thus the advantage of both shunt and series compensation of an AC capacitor can be made use of. The overall result will be an improvement in the voltage and lower losses on the transmission line.

For the system shown in Fig. 3, the series capacitor is connected in the transmission line between the infinite bus and the PCC i.e., in the line between buses 4 and 5. Shunt capacitor is assumed to be connected at the terminals of WECS. Simulations are carried out with shunt compensation alone, series compensation alone and for different combinations of series-shunt compensation.

The results are summarized in Table 1. The results show that, 1) With shunt compensation, there is improvement in voltage profile and decrease in the reactive power demand. The line current reduces thereby reducing transmission losses. The net effect is an improvement in power factor. 2) With series compensation, there is improvement in voltage profile, although there is increase in the reactive power demand. The line current drawn is comparatively large, yet more turbines can be connected on-line. The net effect is an improvement in real power penetration. 3) With series-shunt compensation there is a considerable improvement in voltage profile. At the same time, the reactive power demand and the line current drawn are both reduced compared to series compensation alone and are comparable with shunt compensation.

TABLE I SIMULATION RESULTS AT RATED WIND SPEED (17 M/S)

Type of compensation Capacity V

(PU) P (MW)

Q (MVAR)

I (PU)

Shunt 150 kVAR 200 kVAR 250 kVAR

0.9788 0.9912 1.0031

3.89 3.89 3.89

1.49 1.25 1.01

0.1807 0.1771 0.1729

Series 0.5Xline 0.75Xline

0.9580 1.0090

7.77 7.77

4.43 4.68

0.3604 0.3443

Combined series-shunt

0.5Xline & 150kVAR 0.75Xline & 200kVAR

1.0014 1.0619

7.77 7.77

2.27 1.91

0.1782 0.1253

where, V- voltage at WECS terminals at rated speed, P - Real power generated at rated speed, Q - Reactive power demand at rated speed and I - Transmission line current.

From the results of Table 1 it is seen that higher value of combined series and shunt compensation, produces lower reactive power demand and lesser line current, but the voltage profile becomes too high (>5%). Therefore, it is clear that the combination of series compensation equal to 50% of line reactance and shunt compensation of 150 kVAR, shows better performance for the 9-bus radial system considered.

IV. DYNAMIC ISSUES

The dynamic analysis is necessary (i) to ascertain the wind farm behaviour against various disturbances occurring in the WECS or the grid and (ii) to check whether the induction generators will pick back the load after the fault is isolated. This analysis becomes particularly relevant in cases where the wind energy production has become a significant part of the system production, and consequently the loss of a large part of the wind production in the event of grid faults can have severe consequences for the system stability. Moreover, wind turbine production is often voluntarily reduced at certain times by automatic grid disconnection especially during low consumption periods and when there are strong winds [9]. The purpose is to maintain the stability and reliability of power systems with high wind power penetration. In fact, today wind farms are required to actively participate in power system operation in the same way as conventional power plants. Therefore, power system operators have revised the grid connection requirements for wind farms [10] and now demand that these installations be able to carry out more or less the same control tasks as conventional power plants.

A three-phase fault near the PCC will reduce the terminal voltage at the WECS and increase its speed of rotation. After voltage recovery (fault isolation), the rotor speed of the induction generator may be so high that it does not return to the pre-fault value. The mechanical torque of the turbine will decrease when the turbine speed increases and the turbine may reach the steady state at elevated speed. This state is not desirable since it is accompanied by reduced active power, increased reactive power consumption and reduced voltages near the generating unit. Existing stability concepts used in power system analysis do not include this phenomenon. The phenomenon is however, similar to the motor stalling concept for induction machines in motor operation mode and is termed as rotor speed stability [2].

For the purpose of analysis, the 10 wind turbines at the PCC (bus 9 in Fig. 3) are connected in two groups; Group 1 consisting of 3 turbines aggregated together as one single turbine of capacity 2.25 MW (750 kW x 3) at bus 10 and Group 2 consisting of 7 turbines aggregated together as one single turbine with a capacity of 5.25 MW (750 kW x 7) at bus 11, as shown in Fig. 4. The line between buses 5 and 9 is a double circuit line. Thus the system considered becomes a 11-bus radial system.

58

Fig. 4 Single line diagram of 11-bus radial system

The rotor speed stability analysis is carried out by

evaluating the transient stability of the system [11]. The time response of rotor speed of induction generators and PCC voltage is obtained. One particular case, as described below, is analysed here as it leads to rotor speed instability:

A solid three-phase to ground fault on one of the interconnecting lines between the wind farm PCC (bus 9) and the grid (bus 5) near bus 9 at one second followed by tripping of faulted line between buses 9 and 5 after a delay of 6 cycles when the WECS is operating at rated speed (17 m/s).

Fig. 5 and Fig. 6 show the voltage at the PCC and the rotor speed of WECS respectively. It is seen that the PCC voltage drops to a very low value of 0.1 p.u. initially and does not recover. It settles down at a low value of 0.6 p.u. From Fig. 6, it is seen that the speed of the induction generators monotonically increases which indicates clear instability.

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5TIME (SEC)

PCC

VO

LTA

GE

(PU

)

Fig. 5 PCC voltage for a solid three-phase to ground fault

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

0 1 2 3 4 5TIME (SEC)

RO

TOR

SPE

ED (P

U)

Fig. 6 Rotor speed oscillations of WECS for a solid three-phase to ground

fault

V. DYNAMIC REACTIVE POWER COMPENSATION

Many authors have discussed the application of flexible AC transmission system (FACTS) controllers like static var compensator (SVC) and static synchronous compensator (STATCOM) to improve the voltage ride-through of induction generators [12–19]. It can be understood that these devices do not provide damping of speed oscillations. Hence, in this paper, the effect of unified power flow controller (UPFC) to enhance the rotor speed stability of fixed speed wind turbines is analyzed.

UPFC is a shunt-series connected FACTS controller that can control the various electrical parameters (voltage, real power and reactive power) either individually or simultaneously. For the 11-bus system shown in Fig. 4, simulation is carried out with UPFC connected at the PCC along with 150 kVAR fixed capacitor at each of the generator terminals. A transient model is considered for UPFC [20]. In this paper, fixed capacitor equal to the no-load (operation at cut-in speed) compensation of 150 kVAR is assumed to be connected at the terminals of each generator. Then, the dynamic VAR requirement at the PCC that has to be supplied by UPFC is selected as the difference between full-load (operation at rated speed) and no-load compensation. Thus the UPFC rating is set to ±1.5 MVA (150 kVAR x 10).

The gains of the UPFC are tuned using a simple GA. The objective is minimising the oscillations in PCC voltage and rotor speed. Thus the Sum Squared Deviation Index (SSDI) for UPFC tuning may be written as,

].)()[( 22∑ −+−=k

krefkref VVSSDI ωω (9)

Ignoring the gains in the measurement circuits, there are eight other gains in series and shunt elements of UPFC that are tuned using GA. The assumed gains and the various time constants in the transient model of UPFC [20] are given in Appendix.

It is observed that after tuning, the SSDI is reduced from 0.1124 to 0.0347. The initial values of the gains that are tuned and their optimum values are given in Table 2. With these gains, the same fault simulated in section 4 is considered in this section with UPFC and comparative results with and without UPFC are presented.

TABLE II

UNTUNED AND TUNED GAINS OF UPFC Gain parameters

Untuned Gains

Tuned Gains

K 10 7.6932 KD 10 9.7652 KPdc 10 6.4625 KIdc 1 0.4369 KPP 10 2.6936 KIP 1 0.0498 KPQ 10 5.2894 KIQ 1 0.3836

Fig. 7–9 show the voltage, real power generated and

reactive power demand at the PCC, respectively, with and without UPFC. Fig. 10 shows the rotor speed of induction

59

generators with and without UPFC. It is observed that the induction generators get stabilized and regain their original speed after fault clearance.

Fig. 7 PCC voltage with and without UPFC for a three-phase fault

Fig. 8 Real power at PCC with and without UPFC for a three phase fault

Fig. 9 Reactive power demand at PCC with and without UPFC for a three

phase fault

Fig. 10 Rotor speed of Group 2 with and without UPFC for a three phase fault

Fig. 7 shows that the PCC voltage settles down at 1 p.u. in contrast to 0.6 p.u. without UPFC. The initial transient voltage drop increases to 0.93 p.u. with UPFC. Fig. 8 shows that the real power reduces to zero without UPFC, but with UPFC the power generation by WECS is restored. Similarly, Fig. 9 shows that without UPFC the reactive power demand is very high due to the fault, which reduces substantially once the UPFC is connected.

VI. CONCLUSION

A methodology to investigate the influence of wind power on the operation of power system is presented in this paper. Simulation studies are done on a radial system using C++ programming language. A simultaneous method of power flow technique is used for analyzing the steady state performance of the WECS. The effect of different types of compensation, namely, shunt, series and series-shunt is studied. It is concluded that with a combined series-shunt compensation there is a considerable improvement in voltage profile. At the same time, the reactive power demand and the line current drawn are both reduced compared to operation only with series compensation and are comparable with shunt compensation. A combination of series compensation equal to 50% of line reactance and shunt compensation of 150 kVAR shows better performance as compared to either series or shunt compensation alone, for the analysed 9-bus radial system. Thus with the correct choice of capacitor sizes, a combination of series and shunt compensation can be used to improve the steady state performance. The dynamic performance of the system is explored using rotor speed stability analysis. The effect of UPFC, which is a series-shunt controller, in improving the dynamic performance is examined. It is seen that a dynamic compensation with ±1.5MVA UPFC at the PCC along with a 150 kVAR fixed capacitor at the generator terminals provides the best solution for the analysed 11-bus radial system. In summary, it is recommended that for improving both the steady state and dynamic performances, it is better to go in for series-shunt compensation, rather than the usual practice of using shunt compensation alone. The study also reveals that in certain cases, adequate VAR compensation can be achieved by using the existing capacitor banks along with the FACTS controllers. This way the rating of the FACTS controllers can be reduced. This will lead to a considerable reduction in cost, as the FACTS controllers are very expensive. Moreover, total dispensing of the existing capacitor banks can be avoided.

APPENDIX

Constants in Simultaneous power flow equation

)2

22

(/

mss

rm

XXRsRXVA

++= ⎟

⎠⎞

⎜⎝⎛ +=

sRR

sRB r

xr2

( )22

rxr

x XXs

RRC ++⎟⎠⎞

⎜⎝⎛ += 2)08.0( θλ +=D

60

532 CCCE −−Λ= θ 31035.0

008.011

θθλ −−

+=

Λ

where,

)()(

xss

rsmxx XXjR

jXRjXjXR++

+=+

and V-terminal voltage, Rs-stator resistance, Rr-rotor resistance, Xs-stator leakage reactance, Xr-rotor leakage reactance, Xm-magnetizing reactance of the induction machine, λ-tip speed ratio, θ-pitch angle and C2, C3, and C5 are constants in power coefficient equation [4].

UPFC data All data are in p.u on a 25 MVA and 15 kV base. Rsh : 0; Xsh : 0.025; Rse: 0; Xse : 0.0025; RC : 0.077; KPP : 10; KIP : 1; K : 10; KMP : 1; T1 : 1; TMP : 0.01; KD : 10; KPQ : 10; T2 : 0.01; KIQ : 1; KMac : 1 ; KMQ : 1; TMac : 0.01 ; TMQ : 0.01; KP : 10 ; KI : 1; KMdc : 10; TMdc : 0.01

ACKNOWLEDGMENT The authors wish to acknowledge the support provided by Anna University, India for carrying out this research.

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